Benabdallah, Imane; Benterki, Rebiha; Llibre, Jaume Limit cycles of discontinuous piecewise differential systems separated by a straight line and formed by cubic reversible isochronous centers having rational first integrals. (English) Zbl 07817013 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 31, No. 1, 1-23 (2024). MSC: 34C29 34C25 47H11 PDFBibTeX XMLCite \textit{I. Benabdallah} et al., Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 31, No. 1, 1--23 (2024; Zbl 07817013) Full Text: Link Link
Jimenez, Johana; Llibre, Jaume Limit cycles of polynomial differential systems of degree 1 and 2 on the cylinder. (English) Zbl 07786993 São Paulo J. Math. Sci. 17, No. 2, 679-691 (2023). MSC: 34C05 34C07 34C25 34C40 PDFBibTeX XMLCite \textit{J. Jimenez} and \textit{J. Llibre}, São Paulo J. Math. Sci. 17, No. 2, 679--691 (2023; Zbl 07786993) Full Text: DOI
de Carvalho Braga, Denis; Dias, Fabio Scalco; Llibre, Jaume; Mello, Luis Fernando The discontinuous matching of two globally asymptotically stable crossing piecewise smooth systems in the plane do not produce in general a piecewise differential system globally asymptotically stable. (English) Zbl 07786992 São Paulo J. Math. Sci. 17, No. 2, 671-678 (2023). Reviewer: Paulo Santana (São José do Rio Preto) MSC: 34D23 34A36 34C05 PDFBibTeX XMLCite \textit{D. de Carvalho Braga} et al., São Paulo J. Math. Sci. 17, No. 2, 671--678 (2023; Zbl 07786992) Full Text: DOI
Barkat, Meriem; Benterki, Rebiha; Llibre, Jaume The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems. (English) Zbl 1523.34043 Nonlinear Dyn. 111, No. 2, 1475-1484 (2023). MSC: 34C29 34C25 47H11 PDFBibTeX XMLCite \textit{M. Barkat} et al., Nonlinear Dyn. 111, No. 2, 1475--1484 (2023; Zbl 1523.34043) Full Text: DOI
Llibre, Jaume; Valls, Claudia Reversible global centres with quintic homogeneous nonlinearities. (English) Zbl 1528.34034 Dyn. Syst. 38, No. 4, 632-653 (2023). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C05 34C14 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Dyn. Syst. 38, No. 4, 632--653 (2023; Zbl 1528.34034) Full Text: DOI
Li, Shimin; Liu, Changjian; Llibre, Jaume On the Poincaré-Bendixson formula for planar piecewise smooth vector fields. (English) Zbl 1527.34038 J. Nonlinear Sci. 33, No. 6, Paper No. 118, 29 p. (2023). Reviewer: Zhengdong Du (Chengdu) MSC: 34A36 34C05 PDFBibTeX XMLCite \textit{S. Li} et al., J. Nonlinear Sci. 33, No. 6, Paper No. 118, 29 p. (2023; Zbl 1527.34038) Full Text: DOI
Llibre, Jaume; Valls, Claudia The 16th Hilbert problem for discontinuous piecewise linear differential systems separated by the algebraic curve \(y = x^n\). (English) Zbl 07749839 Math. Phys. Anal. Geom. 26, No. 4, Paper No. 25, 9 p. (2023). Reviewer: Alexander Grin (Grodno) MSC: 34C07 34A36 34A30 34C05 34C23 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Math. Phys. Anal. Geom. 26, No. 4, Paper No. 25, 9 p. (2023; Zbl 07749839) Full Text: DOI
Li, Tao; Llibre, Jaume On the 16th Hilbert problem for discontinuous piecewise polynomial Hamiltonian systems. (English) Zbl 07735757 J. Dyn. Differ. Equations 35, No. 1, 87-102 (2023). MSC: 34A36 34C07 34C29 34C05 PDFBibTeX XMLCite \textit{T. Li} and \textit{J. Llibre}, J. Dyn. Differ. Equations 35, No. 1, 87--102 (2023; Zbl 07735757) Full Text: DOI
Llibre, Jaume; Teixeira, Marco Antonio On the periodic orbits of the continuous-discontinuous piecewise differential systems with three pieces separated by two parallel straight lines. (English) Zbl 1518.34053 Commun. Nonlinear Sci. Numer. Simul. 125, Article ID 107421, 9 p. (2023). MSC: 34C29 34C25 47H11 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{M. A. Teixeira}, Commun. Nonlinear Sci. Numer. Simul. 125, Article ID 107421, 9 p. (2023; Zbl 1518.34053) Full Text: DOI
Benabdallah, Imane; Benterki, Rebiha; Llibre, Jaume The limit cycles of a class of piecewise differential systems. (English) Zbl 07730206 Bol. Soc. Mat. Mex., III. Ser. 29, No. 3, Paper No. 62, 45 p. (2023). MSC: 34A36 34C07 34C05 34C29 34C25 47H11 PDFBibTeX XMLCite \textit{I. Benabdallah} et al., Bol. Soc. Mat. Mex., III. Ser. 29, No. 3, Paper No. 62, 45 p. (2023; Zbl 07730206) Full Text: DOI
Llibre, Jaume; Valls, Clàudia The Markus-Yamabe conjecture for discontinuous piecewise linear differential systems in \(\mathbb{R}^n\) separated by a \(\mathrm{conic} \!\times \! \mathbb{R}^{n-2}\). (English) Zbl 1526.34012 J. Dyn. Differ. Equations 35, No. 3, 2579-2588 (2023). Reviewer: George Karakostas (Ioannina) MSC: 34A36 34A30 34C05 34D23 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, J. Dyn. Differ. Equations 35, No. 3, 2579--2588 (2023; Zbl 1526.34012) Full Text: DOI
Benterki, Rebiha; Llibre, Jaume On the limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves. III. (English) Zbl 1518.34052 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 30, No. 1, 35-77 (2023). MSC: 34C29 34C25 47H11 PDFBibTeX XMLCite \textit{R. Benterki} and \textit{J. Llibre}, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 30, No. 1, 35--77 (2023; Zbl 1518.34052) Full Text: Link Link
Llibre, Jaume Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center. (English) Zbl 1512.34069 Discrete Contin. Dyn. Syst., Ser. S 16, No. 3-4, 533-547 (2023). MSC: 34C05 34C07 37G15 PDFBibTeX XMLCite \textit{J. Llibre}, Discrete Contin. Dyn. Syst., Ser. S 16, No. 3--4, 533--547 (2023; Zbl 1512.34069) Full Text: DOI
Anacleto, Maria Elisa; Llibre, Jaume; Valls, Claudia; Vidal, Claudio Crossing limit cycles for discontinuous piecewise linear differential centers separated by three parallel straight lines. (English) Zbl 1520.34024 Rend. Circ. Mat. Palermo (2) 72, No. 3, 1739-1750 (2023). Reviewer: Zhengdong Du (Chengdu) MSC: 34C05 34C07 34A36 34A30 PDFBibTeX XMLCite \textit{M. E. Anacleto} et al., Rend. Circ. Mat. Palermo (2) 72, No. 3, 1739--1750 (2023; Zbl 1520.34024) Full Text: DOI
Anacleto, Maria Elisa; Llibre, Jaume; Valls, Claudia; Vidal, Claudio Limit cycles of a continuous piecewise differential system formed by a quadratic center and two linear centers. (English) Zbl 1528.34030 Bol. Soc. Mat. Mex., III. Ser. 29, No. 2, Paper No. 29, 12 p. (2023). Reviewer: Xiuli Cen (Zhuhai) MSC: 34C05 34C07 34A05 34A36 PDFBibTeX XMLCite \textit{M. E. Anacleto} et al., Bol. Soc. Mat. Mex., III. Ser. 29, No. 2, Paper No. 29, 12 p. (2023; Zbl 1528.34030) Full Text: DOI
Llibre, Jaume; Valls, Claudia Global phase portraits of the generalized van der Pol systems. (English) Zbl 1518.34039 Bull. Sci. Math. 182, Article ID 103213, 19 p. (2023). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Bull. Sci. Math. 182, Article ID 103213, 19 p. (2023; Zbl 1518.34039) Full Text: DOI
Chen, Ting; Li, Shimin; Llibre, Jaume Nilpotent bi-center in continuous piecewise \(\mathbb{Z}_2\)-equivariant cubic polynomial Hamiltonian systems. (English) Zbl 1519.34032 Nonlinear Dyn. 110, No. 1, 705-721 (2022). MSC: 34C25 34A36 37J12 70H12 PDFBibTeX XMLCite \textit{T. Chen} et al., Nonlinear Dyn. 110, No. 1, 705--721 (2022; Zbl 1519.34032) Full Text: DOI
Llibre, Jaume; Valls, Claudia Crossing limit cycles for discontinuous piecewise differential systems formed by linear Hamiltonian saddles or linear centers separated by a conic. (English) Zbl 1505.34047 Chaos Solitons Fractals 159, Article ID 112076, 8 p. (2022). MSC: 34C05 34A36 37G15 34C23 34C07 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Chaos Solitons Fractals 159, Article ID 112076, 8 p. (2022; Zbl 1505.34047) Full Text: DOI
Llibre, Jaume; Salhi, Tayeb On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center. (English) Zbl 1504.34072 Chaos Solitons Fractals 160, Article ID 112256, 6 p. (2022). MSC: 34C05 34A36 34C07 37G15 34C23 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{T. Salhi}, Chaos Solitons Fractals 160, Article ID 112256, 6 p. (2022; Zbl 1504.34072) Full Text: DOI
Giné, Jaume; Grau, Maite; Llibre, Jaume Criteria on the existence of limit cycles in planar polynomial differential systems. (English) Zbl 1517.34039 Expo. Math. 40, No. 4, 1049-1083 (2022). Reviewer: Alexander Grin (Grodno) MSC: 34C05 34C07 34C20 PDFBibTeX XMLCite \textit{J. Giné} et al., Expo. Math. 40, No. 4, 1049--1083 (2022; Zbl 1517.34039) Full Text: DOI
Jimenez, Johana; Llibre, Jaume; Valls, Claudia Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by nonregular curves. (English) Zbl 07614853 Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 12, Article ID 2250184, 23 p. (2022). MSC: 34A36 34C05 34A30 37J20 PDFBibTeX XMLCite \textit{J. Jimenez} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 12, Article ID 2250184, 23 p. (2022; Zbl 07614853) Full Text: DOI
Villanueva, Yovani; Llibre, Jaume; Euzébio, Rodrigo Limit cycles of generic piecewise center-type vector fields in \(\mathbb{R}^3\) separated by either one plane or by two parallel planes. (English) Zbl 1505.37060 Bull. Sci. Math. 179, Article ID 103173, 14 p. (2022). Reviewer: Zhengdong Du (Chengdu) MSC: 37G15 37C75 34C05 34A36 37M05 PDFBibTeX XMLCite \textit{Y. Villanueva} et al., Bull. Sci. Math. 179, Article ID 103173, 14 p. (2022; Zbl 1505.37060) Full Text: DOI
Chen, Ting; Llibre, Jaume Nilpotent center in a continuous piecewise quadratic polynomial Hamiltonian vector field. (English) Zbl 1510.37090 Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 8, Article ID 2250116, 23 p. (2022). Reviewer: Tudor Bînzar (Timişoara) MSC: 37J25 37J39 34A36 34C05 34C07 70H05 PDFBibTeX XMLCite \textit{T. Chen} and \textit{J. Llibre}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 8, Article ID 2250116, 23 p. (2022; Zbl 1510.37090) Full Text: DOI
Jimenez, Jeidy J.; Llibre, Jaume; Medrado, Joo C. On the crossing limit cycles for piecewise linear differential systems separated by a straight line and having symmetric equilibrium points. (English) Zbl 1490.34032 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 29, No. 4, 253-283 (2022). MSC: 34C05 34C07 37G15 PDFBibTeX XMLCite \textit{J. J. Jimenez} et al., Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 29, No. 4, 253--283 (2022; Zbl 1490.34032) Full Text: Link Link
Ghermoul, Bilal; Llibre, Jaume; Salhi, Tayeb Limit cycles of piecewise-continuous differential systems formed by linear and quadratic isochronous centers II. (English) Zbl 1504.34064 Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 6, Article ID 2250091, 33 p. (2022). MSC: 34C05 34A36 34C07 34C23 PDFBibTeX XMLCite \textit{B. Ghermoul} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 6, Article ID 2250091, 33 p. (2022; Zbl 1504.34064) Full Text: DOI
Llibre, Jaume; Valls, Claudia Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres. (English) Zbl 1504.34073 Dyn. Syst. 37, No. 2, 262-279 (2022). Reviewer: Adriana Buică (Cluj-Napoca) MSC: 34C05 34C23 34C07 34C29 34A36 34A30 34A05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Dyn. Syst. 37, No. 2, 262--279 (2022; Zbl 1504.34073) Full Text: DOI
Ghermoul, Bilal; Llibre, Jaume; Salhi, Tayeb Limit cycles of continuous piecewise differential systems formed by linear and quadratic isochronous centers I. (English) Zbl 1497.34056 Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 1, Article ID 2250003, 28 p. (2022). Reviewer: Qinlong Wang (Guilin) MSC: 34C05 34A36 34A05 34C07 34C23 PDFBibTeX XMLCite \textit{B. Ghermoul} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 1, Article ID 2250003, 28 p. (2022; Zbl 1497.34056) Full Text: DOI
Diz-Pita, Érika; Llibre, Jaume; Otero-Espinar, M. Victoria Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity. (English) Zbl 1482.34122 Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 106038, 16 p. (2022). MSC: 34C60 92D25 34C05 PDFBibTeX XMLCite \textit{É. Diz-Pita} et al., Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 106038, 16 p. (2022; Zbl 1482.34122) Full Text: DOI
Belfar, Ahlam; Benterki, Rebiha; Llibre, Jaume Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibrium points and separated by irreducible cubics. (English) Zbl 1479.34077 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 28, No. 6, 399-421 (2021). MSC: 34C29 34C25 47H11 PDFBibTeX XMLCite \textit{A. Belfar} et al., Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 28, No. 6, 399--421 (2021; Zbl 1479.34077) Full Text: Link
Esteban, Marina; Llibre, Jaume; Valls, Claudia The extended 16th Hilbert problem for discontinuous piecewise linear centers separated by a nonregular line. (English) Zbl 1490.34036 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 15, Article ID 2150225, 10 p. (2021). Reviewer: Xingwu Chen (Chengdu) MSC: 34C07 34C05 34A36 34C23 PDFBibTeX XMLCite \textit{M. Esteban} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 15, Article ID 2150225, 10 p. (2021; Zbl 1490.34036) Full Text: DOI
Carvalho, Tiago; Gonçalves, Luiz Fernando; Llibre, Jaume Limit cycles on piecewise smooth vector fields with coupled rigid centers. (English) Zbl 1489.34048 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 15, Article ID 2150224, 19 p. (2021). Reviewer: Zhengdong Du (Chengdu) MSC: 34C05 34C07 34C23 34A36 34C25 PDFBibTeX XMLCite \textit{T. Carvalho} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 15, Article ID 2150224, 19 p. (2021; Zbl 1489.34048) Full Text: DOI
Li, Tao; Llibre, Jaume Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems. (English) Zbl 1487.34001 Expo. Math. 39, No. 4, 540-565 (2021). Reviewer: Joan C. Artés (Barcelona) MSC: 34-02 34-00 34C05 PDFBibTeX XMLCite \textit{T. Li} and \textit{J. Llibre}, Expo. Math. 39, No. 4, 540--565 (2021; Zbl 1487.34001) Full Text: DOI
Diz-Pita, Érika; Llibre, Jaume; Otero-Espinar, M. Victoria Planar Kolmogorov systems coming from spatial Lotka-Volterra systems. (English) Zbl 1490.34030 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 13, Article ID 2150201, 37 p. (2021). Reviewer: Valentine Tyshchenko (Grodno) MSC: 34C05 34A05 34C20 PDFBibTeX XMLCite \textit{É. Diz-Pita} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 13, Article ID 2150201, 37 p. (2021; Zbl 1490.34030) Full Text: DOI
Llibre, Jaume; Zhang, Xiang The Markus-Yamabe conjecture for continuous and discontinuous piecewise linear differential systems. (English) Zbl 1489.34083 Proc. Am. Math. Soc. 149, No. 12, 5267-5274 (2021). Reviewer: David Cheban (Chişinău) MSC: 34D23 34D45 34A30 34A36 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, Proc. Am. Math. Soc. 149, No. 12, 5267--5274 (2021; Zbl 1489.34083) Full Text: DOI
Llibre, Jaume; Zhang, Xiang A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems. (English) Zbl 1481.34041 Expo. Math. 39, No. 1, 48-61 (2021). Reviewer: Alexander Grin (Grodno) MSC: 34C05 34C07 34C29 34A36 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, Expo. Math. 39, No. 1, 48--61 (2021; Zbl 1481.34041) Full Text: DOI
Diz-Pita, Érika; Llibre, Jaume; Otero-Espinar, M. Victoria Phase portraits of a family of Kolmogorov systems depending on six parameters. (English) Zbl 1462.34049 Electron. J. Differ. Equ. 2021, Paper No. 35, 38 p. (2021). MSC: 34C05 PDFBibTeX XMLCite \textit{É. Diz-Pita} et al., Electron. J. Differ. Equ. 2021, Paper No. 35, 38 p. (2021; Zbl 1462.34049) Full Text: Link
Benterki, Rebiha; Llibre, Jaume The limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves I. (English) Zbl 1477.34035 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 28, No. 3, 153-192 (2021). Reviewer: Jeidy Johana Jimenez (Goiânia) MSC: 34A36 34C05 34C29 47H11 34C07 PDFBibTeX XMLCite \textit{R. Benterki} and \textit{J. Llibre}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 28, No. 3, 153--192 (2021; Zbl 1477.34035) Full Text: Link
Anacleto, Maria Elisa; Llibre, Jaume; Valls, Claudia; Vidal, Claudio Limit cycles of discontinuous piecewise differential systems formed by linear centers in \(\mathbb{R}^2\) and separated by two circles. (English) Zbl 1468.34021 Nonlinear Anal., Real World Appl. 60, Article ID 103281, 12 p. (2021). MSC: 34A36 34A05 34C05 34C07 PDFBibTeX XMLCite \textit{M. E. Anacleto} et al., Nonlinear Anal., Real World Appl. 60, Article ID 103281, 12 p. (2021; Zbl 1468.34021) Full Text: DOI
Benterki, Rebiha; Llibre, Jaume The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems. (English) Zbl 1517.34060 Nonlinear Dyn. 102, No. 4, 2453-2466 (2020). MSC: 34C29 34C25 47H11 34A36 PDFBibTeX XMLCite \textit{R. Benterki} and \textit{J. Llibre}, Nonlinear Dyn. 102, No. 4, 2453--2466 (2020; Zbl 1517.34060) Full Text: DOI
Cardoso, João L.; Llibre, Jaume; Novaes, Douglas D.; Tonon, Durval J. Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields. (English) Zbl 1479.34057 Dyn. Syst. 35, No. 3, 490-514 (2020). Reviewer: Xiuli Cen (Zhuhai) MSC: 34C05 34C07 34C23 34A36 34E10 PDFBibTeX XMLCite \textit{J. L. Cardoso} et al., Dyn. Syst. 35, No. 3, 490--514 (2020; Zbl 1479.34057) Full Text: DOI arXiv
da Fonseca, Alexander Fernandes; Llibre, Jaume; Mello, Luis Fernando Limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points. (English) Zbl 1453.34047 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 11, Article ID 2050157, 8 p. (2020). Reviewer: Jeidy Johana Jimenez (Goiânia) MSC: 34C07 34A36 34C05 PDFBibTeX XMLCite \textit{A. F. da Fonseca} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 11, Article ID 2050157, 8 p. (2020; Zbl 1453.34047) Full Text: DOI
Llibre, Jaume On the centers of cubic polynomial differential systems with four invariant straight lines. (English) Zbl 1454.34054 Topol. Methods Nonlinear Anal. 55, No. 2, 387-402 (2020). Reviewer: Jihua Yang (Guyuan) MSC: 34C05 34C07 34C45 PDFBibTeX XMLCite \textit{J. Llibre}, Topol. Methods Nonlinear Anal. 55, No. 2, 387--402 (2020; Zbl 1454.34054) Full Text: DOI Euclid
Llibre, Jaume; Oliveira, Regilene D.; Rodrigues, Camila Ap. B. Limit cycles for two classes of control piecewise linear differential systems. (English) Zbl 1457.37068 São Paulo J. Math. Sci. 14, No. 1, 49-65 (2020). Reviewer: Fengqin Zhang (Yuncheng) MSC: 37G15 34C07 34C05 34C23 34C29 PDFBibTeX XMLCite \textit{J. Llibre} et al., São Paulo J. Math. Sci. 14, No. 1, 49--65 (2020; Zbl 1457.37068) Full Text: DOI arXiv
Llibre, Jaume Limit cycles in continuous and discontinuous piecewise linear differential systems with two pieces separated by a straight line. (English) Zbl 1474.34224 Bul. Acad. Științe Repub. Mold., Mat. 2019, No. 2(90), 3-12 (2019). MSC: 34C05 34A36 PDFBibTeX XMLCite \textit{J. Llibre}, Bul. Acad. Științe Repub. Mold., Mat. 2019, No. 2(90), 3--12 (2019; Zbl 1474.34224) Full Text: Link
Llibre, Jaume; Salhi, Tayeb The limit cycles of a class of quintic polynomial vector fields. (English) Zbl 1453.34042 Topol. Methods Nonlinear Anal. 54, No. 1, 141-151 (2019). Reviewer: Alexander Grin (Grodno) MSC: 34C05 34A34 34C07 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{T. Salhi}, Topol. Methods Nonlinear Anal. 54, No. 1, 141--151 (2019; Zbl 1453.34042) Full Text: DOI Euclid
Llibre, Jaume; Salhi, Tayeb On the limit cycles surrounding a diagonalizable linear node with homogeneous nonlinearities. (English) Zbl 1435.34035 Appl. Math. Lett. 98, 427-431 (2019). Reviewer: Alexander Grin (Grodno) MSC: 34C07 34C05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{T. Salhi}, Appl. Math. Lett. 98, 427--431 (2019; Zbl 1435.34035) Full Text: DOI Link
Llibre, Jaume; Zhang, Xiang Limit cycles created by piecewise linear centers. (English) Zbl 1506.34047 Chaos 29, No. 5, 053116, 14 p. (2019). MSC: 34C05 34A36 34A30 34C23 34C07 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, Chaos 29, No. 5, 053116, 14 p. (2019; Zbl 1506.34047) Full Text: DOI Link
Llibre, Jaume; Tang, Yilei Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. (English) Zbl 1478.34040 Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1769-1784 (2019). Reviewer: Stefano Marò (Pisa) MSC: 34C07 34C29 34C25 34C05 34A36 34E10 34C23 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{Y. Tang}, Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1769--1784 (2019; Zbl 1478.34040) Full Text: DOI arXiv
Llibre, Jaume; Zhang, Xiang Limit cycles for discontinuous planar piecewise linear differential systems separated by an algebraic curve. (English) Zbl 1414.34023 Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 2, Article ID 1950017, 17 p. (2019). MSC: 34C05 34A36 34C20 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 2, Article ID 1950017, 17 p. (2019; Zbl 1414.34023) Full Text: DOI
Llibre, Jaume; Martínez, Y. Paulina; Vidal, Claudio Phase portraits of linear type centers of polynomial Hamiltonian systems with Hamiltonian function of degree 5 of the form \(H = H_1(x)+H_2(y)\). (English) Zbl 1412.37059 Discrete Contin. Dyn. Syst. 39, No. 1, 75-113 (2019). Reviewer: Cristian Lăzureanu (Timisoara) MSC: 37J25 37C15 37C10 34C07 70K05 PDFBibTeX XMLCite \textit{J. Llibre} et al., Discrete Contin. Dyn. Syst. 39, No. 1, 75--113 (2019; Zbl 1412.37059) Full Text: DOI
Llibre, Jaume; Zhang, Xiang Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center. (English) Zbl 1411.34030 J. Math. Anal. Appl. 467, No. 1, 537-549 (2018). Reviewer: Alexander Grin (Grodno) MSC: 34A36 34C05 34C20 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, J. Math. Anal. Appl. 467, No. 1, 537--549 (2018; Zbl 1411.34030) Full Text: DOI Link
Llibre, Jaume; Teixeira, Marco Antonio Periodic orbits of continuous and discontinuous piecewise linear differential systems via first integrals. (English) Zbl 1395.34049 São Paulo J. Math. Sci. 12, No. 1, 121-135 (2018). MSC: 34C25 34C29 47H11 34A36 34A05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{M. A. Teixeira}, São Paulo J. Math. Sci. 12, No. 1, 121--135 (2018; Zbl 1395.34049) Full Text: DOI Link
Llibre, Jaume; Teixeira, Marco Antonio Piecewise linear differential systems with only centers can create limit cycles? (English) Zbl 1390.34081 Nonlinear Dyn. 91, No. 1, 249-255 (2018). MSC: 34C05 34A36 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{M. A. Teixeira}, Nonlinear Dyn. 91, No. 1, 249--255 (2018; Zbl 1390.34081) Full Text: DOI Link
Llibre, Jaume; Lopes, Bruno D.; De Moraes, Jaime R. Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3. (English) Zbl 1422.34122 Electron. J. Differ. Equ. 2018, Paper No. 118, 14 p. (2018). Reviewer: Valery Romanovski (Maribor) MSC: 34C07 34C23 34C25 34C29 37G15 PDFBibTeX XMLCite \textit{J. Llibre} et al., Electron. J. Differ. Equ. 2018, Paper No. 118, 14 p. (2018; Zbl 1422.34122) Full Text: Link
de Freitas, Bruno R.; Llibre, Jaume; Medrado, Joao C. Limit cycles of continuous and discontinuous piecewise-linear differential systems in \(\mathbb{R}^3\). (English) Zbl 1390.34083 J. Comput. Appl. Math. 338, 311-323 (2018). Reviewer: Anthony D. Osborne (Keele) MSC: 34C05 34C07 37G15 34A36 34C29 PDFBibTeX XMLCite \textit{B. R. de Freitas} et al., J. Comput. Appl. Math. 338, 311--323 (2018; Zbl 1390.34083) Full Text: DOI
Llibre, Jaume; Teixeira, Marco Antonio Piecewise linear differential systems without equilibria produce limit cycles? (English) Zbl 1373.34050 Nonlinear Dyn. 88, No. 1, 157-164 (2017). MSC: 34C05 34A36 34C29 34C25 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{M. A. Teixeira}, Nonlinear Dyn. 88, No. 1, 157--164 (2017; Zbl 1373.34050) Full Text: DOI Link
Chen, Xingwu; Llibre, Jaume; Wang, Zhaoxia; Zhang, Weinian Restricted independence in displacement function for better estimation of cyclicity. (English) Zbl 1375.34045 J. Differ. Equations 262, No. 12, 5773-5791 (2017). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34C05 34C07 34C23 PDFBibTeX XMLCite \textit{X. Chen} et al., J. Differ. Equations 262, No. 12, 5773--5791 (2017; Zbl 1375.34045) Full Text: DOI Link
Colak, Ilker E.; Llibre, Jaume; Valls, Claudia On the bifurcation of limit cycles due to polynomial perturbations of Hamiltonian centers. (English) Zbl 1375.34063 Mediterr. J. Math. 14, No. 2, Paper No. 40, 10 p. (2017). Reviewer: Jaume Giné (Lleida) MSC: 34C23 34C05 34E10 34C07 37J45 PDFBibTeX XMLCite \textit{I. E. Colak} et al., Mediterr. J. Math. 14, No. 2, Paper No. 40, 10 p. (2017; Zbl 1375.34063) Full Text: DOI Link
de Carvalho, Tiago; Llibre, Jaume; Tonon, Durval José Limit cycles of discontinuous piecewise polynomial vector fields. (English) Zbl 1382.37048 J. Math. Anal. Appl. 449, No. 1, 572-579 (2017). Reviewer: Valery A. Gaiko (Minsk) MSC: 37G15 34C05 34A36 34C29 PDFBibTeX XMLCite \textit{T. de Carvalho} et al., J. Math. Anal. Appl. 449, No. 1, 572--579 (2017; Zbl 1382.37048) Full Text: DOI Link
Llibre, J.; Lopes, B. D.; de Moraes, J. R. Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2. (English) Zbl 1410.34097 Appl. Math. Comput. 274, 47-54 (2016). MSC: 34C07 34C23 34C25 34C29 37C10 37C27 37G15 PDFBibTeX XMLCite \textit{J. Llibre} et al., Appl. Math. Comput. 274, 47--54 (2016; Zbl 1410.34097) Full Text: DOI Link
Llibre, J. Centers: their integrability and relations with the divergence. (English) Zbl 1386.34056 Appl. Math. Nonlinear Sci. 1, No. 1, 79-86 (2016). MSC: 34C05 34A34 PDFBibTeX XMLCite \textit{J. Llibre}, Appl. Math. Nonlinear Sci. 1, No. 1, 79--86 (2016; Zbl 1386.34056) Full Text: DOI
Gouveia, Márcio R. A.; Llibre, Jaume; Novaes, Douglas D. On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems. (English) Zbl 1410.37052 Appl. Math. Comput. 271, 365-374 (2015). MSC: 37G15 34C05 PDFBibTeX XMLCite \textit{M. R. A. Gouveia} et al., Appl. Math. Comput. 271, 365--374 (2015; Zbl 1410.37052) Full Text: DOI Link
Llibre, Jaume; Novaes, Douglas D.; Teixeira, Marco A. On the birth of limit cycles for non-smooth dynamical systems. (English) Zbl 1407.37080 Bull. Sci. Math. 139, No. 3, 229-244 (2015). MSC: 37G15 37C80 37C30 34C07 PDFBibTeX XMLCite \textit{J. Llibre} et al., Bull. Sci. Math. 139, No. 3, 229--244 (2015; Zbl 1407.37080) Full Text: DOI arXiv
Llibre, Jaume; Novaes, Douglas D.; Teixeira, Marco Antonio On the periodic solutions of perturbed 4D non-resonant systems. (English) Zbl 1369.34061 São Paulo J. Math. Sci. 9, No. 2, 229-250 (2015). MSC: 34C25 34C15 34D10 37G15 PDFBibTeX XMLCite \textit{J. Llibre} et al., São Paulo J. Math. Sci. 9, No. 2, 229--250 (2015; Zbl 1369.34061) Full Text: DOI arXiv Link
Llibre, Jaume; Novaes, Douglas D.; Teixeira, Marco A. Maximum number of limit cycles for certain piecewise linear dynamical systems. (English) Zbl 1348.34065 Nonlinear Dyn. 82, No. 3, 1159-1175 (2015). MSC: 34C05 34A36 PDFBibTeX XMLCite \textit{J. Llibre} et al., Nonlinear Dyn. 82, No. 3, 1159--1175 (2015; Zbl 1348.34065) Full Text: DOI Link
Llibre, Jaume; Teixeira, Marco Antonio Limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations. (English) Zbl 1323.34042 Z. Angew. Math. Phys. 66, No. 1, 51-66 (2015). Reviewer: Valery Romanovski (Maribor) MSC: 34C05 34C29 34A36 34C25 47H11 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{M. A. Teixeira}, Z. Angew. Math. Phys. 66, No. 1, 51--66 (2015; Zbl 1323.34042) Full Text: DOI
Llibre, Jaume; Mereu, Ana C.; Novaes, Douglas D. Averaging theory for discontinuous piecewise differential systems. (English) Zbl 1347.37097 J. Differ. Equations 258, No. 11, 4007-4032 (2015). MSC: 37G15 37C80 37C30 PDFBibTeX XMLCite \textit{J. Llibre} et al., J. Differ. Equations 258, No. 11, 4007--4032 (2015; Zbl 1347.37097) Full Text: DOI Link
Euzébio, Rodrigo D.; Llibre, Jaume On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line. (English) Zbl 1309.34039 J. Math. Anal. Appl. 424, No. 1, 475-486 (2015). MSC: 34C05 34A36 PDFBibTeX XMLCite \textit{R. D. Euzébio} and \textit{J. Llibre}, J. Math. Anal. Appl. 424, No. 1, 475--486 (2015; Zbl 1309.34039) Full Text: DOI arXiv
Artés, Joan C.; Llibre, Jaume; Medrado, Joao C.; Teixeira, Marco A. Piecewise linear differential systems with two real saddles. (English) Zbl 07312523 Math. Comput. Simul. 95, 13-22 (2014). MSC: 34C05 34C07 37G15 PDFBibTeX XMLCite \textit{J. C. Artés} et al., Math. Comput. Simul. 95, 13--22 (2014; Zbl 07312523) Full Text: DOI Link
Giné, Jaume; Llibre, Jaume A method for characterizing nilpotent centers. (English) Zbl 1323.34038 J. Math. Anal. Appl. 413, No. 1, 537-545 (2014). Reviewer: A. P. Sadovskii (Minsk) MSC: 34C05 34C23 PDFBibTeX XMLCite \textit{J. Giné} and \textit{J. Llibre}, J. Math. Anal. Appl. 413, No. 1, 537--545 (2014; Zbl 1323.34038) Full Text: DOI Link
Benterki, Rebiha; Llibre, Jaume Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities. (English) Zbl 1314.34065 J. Math. Anal. Appl. 407, No. 1, 16-22 (2013). MSC: 34C07 34C05 34C23 34C29 PDFBibTeX XMLCite \textit{R. Benterki} and \textit{J. Llibre}, J. Math. Anal. Appl. 407, No. 1, 16--22 (2013; Zbl 1314.34065) Full Text: DOI
Llibre, Jaume; Rabanal, Roland Planar real polynomial differential systems of degree \(n> 3\) having a weak focus of high order. (English) Zbl 1254.34048 Rocky Mt. J. Math. 42, No. 2, 657-693 (2012). Reviewer: Valery Romanovski (Maribor) MSC: 34C05 34C07 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{R. Rabanal}, Rocky Mt. J. Math. 42, No. 2, 657--693 (2012; Zbl 1254.34048) Full Text: DOI Euclid
Alavez-Ramírez, Justino; Blé, Gamaliel; Castellanos, Víctor; Llibre, Jaume On the global flow of a 3-dimensional Lotka-Volterra system. (English) Zbl 1246.37075 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 10, 4114-4125 (2012). Reviewer: Adriana Buică (Cluj-Napoca) MSC: 37G15 37D45 PDFBibTeX XMLCite \textit{J. Alavez-Ramírez} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 10, 4114--4125 (2012; Zbl 1246.37075) Full Text: DOI
Cairó, Laurent; Llibre, Jaume Phase portraits of planar semi-homogeneous vector fields. III. (English) Zbl 1270.34107 Qual. Theory Dyn. Syst. 10, No. 2, 203-246 (2011). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C41 34C05 34C14 PDFBibTeX XMLCite \textit{L. Cairó} and \textit{J. Llibre}, Qual. Theory Dyn. Syst. 10, No. 2, 203--246 (2011; Zbl 1270.34107) Full Text: DOI
Llibre, Jaume; Ponce, Enrique; Ros, Javier Algebraic determination of limit cycles in a family of three-dimensional piecewise linear differential systems. (English) Zbl 1232.34047 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 6712-6727 (2011). Reviewer: Svitlana P. Rogovchenko (Umeå) MSC: 34C05 34C25 PDFBibTeX XMLCite \textit{J. Llibre} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 6712--6727 (2011; Zbl 1232.34047) Full Text: DOI Link
Llibre, Jaume; Valls, Clàudia Classification of the centers and their isochronicity for a class of polynomial differential systems of arbitrary degree. (English) Zbl 1230.37028 Adv. Math. 227, No. 1, 472-493 (2011). Reviewer: Dieter Erle (Dortmund) MSC: 37C10 34C07 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Adv. Math. 227, No. 1, 472--493 (2011; Zbl 1230.37028) Full Text: DOI
Llibre, Jaume; Mereu, Ana Cristina Limit cycles for generalized Kukles polynomial differential systems. (English) Zbl 1228.34050 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 4, 1261-1271 (2011). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C05 34C29 34C25 34C23 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{A. C. Mereu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 4, 1261--1271 (2011; Zbl 1228.34050) Full Text: DOI Link
Llibre, Jaume; Valls, Clàudia Centers and isochronous centers for two classes of generalized seventh and ninth systems. (English) Zbl 1222.34032 J. Dyn. Differ. Equations 22, No. 4, 657-675 (2010). Reviewer: Armengol Gasull (Barcelona) MSC: 34C05 34C25 37C27 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, J. Dyn. Differ. Equations 22, No. 4, 657--675 (2010; Zbl 1222.34032) Full Text: DOI Link
Cobo, Milton; Gutierrez, Carlos; Llibre, Jaume Flows without wandering points on compact connected surfaces. (English) Zbl 1203.37025 Trans. Am. Math. Soc. 362, No. 9, 4569-4580 (2010). Reviewer: I. V. Boikov (Penza) MSC: 37B10 PDFBibTeX XMLCite \textit{M. Cobo} et al., Trans. Am. Math. Soc. 362, No. 9, 4569--4580 (2010; Zbl 1203.37025) Full Text: DOI
Coll, Bartomeu; Ferragut, Antoni; Llibre, Jaume Polynomial inverse integrating factors for quadratic differential systems. (English) Zbl 1203.34063 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 4, 881-914 (2010). Reviewer: Alexey Remizov (Trieste) MSC: 34C20 34C05 34C07 34A05 PDFBibTeX XMLCite \textit{B. Coll} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 4, 881--914 (2010; Zbl 1203.34063) Full Text: DOI
Llibre, Jaume; Pessoa, Claudio Phase portraits for quadratic homogeneous polynomial vector fields on \(\mathbb S^{2}\). (English) Zbl 1196.34040 Rend. Circ. Mat. Palermo (2) 58, No. 3, 361-406 (2009). Reviewer: Iliya Iliev (Sofia) MSC: 34C07 34C05 34C23 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Pessoa}, Rend. Circ. Mat. Palermo (2) 58, No. 3, 361--406 (2009; Zbl 1196.34040) Full Text: DOI arXiv
Llibre, Jaume; Valls, Clàudia Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems. (English) Zbl 1195.34046 NoDEA, Nonlinear Differ. Equ. Appl. 16, No. 5, 657-679 (2009). Reviewer: Alexander Grin (Grodno) MSC: 34C05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, NoDEA, Nonlinear Differ. Equ. Appl. 16, No. 5, 657--679 (2009; Zbl 1195.34046) Full Text: DOI
Llibre, Jaume; Pessoa, Claudio On the centers of the weight-homogeneous polynomial vector fields on the plane. (English) Zbl 1180.34030 J. Math. Anal. Appl. 359, No. 2, 722-730 (2009). Reviewer: Gheorghe Tigan (Timisoara) MSC: 34C05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Pessoa}, J. Math. Anal. Appl. 359, No. 2, 722--730 (2009; Zbl 1180.34030) Full Text: DOI arXiv Link
Llibre, Jaume; Valls, Clàudia Classification of the centers and isochronous centers for a class of quartic-like systems. (English) Zbl 1201.34051 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7-8, 3119-3128 (2009). Reviewer: Liqin Zhao (Beijing) MSC: 34C05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7--8, 3119--3128 (2009; Zbl 1201.34051) Full Text: DOI
Llibre, Jaume; Valls, Clàudia Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems. (English) Zbl 1190.34033 J. Math. Anal. Appl. 357, No. 2, 427-437 (2009). Reviewer: A. P. Sadovskii (Minsk) MSC: 34C05 34C23 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, J. Math. Anal. Appl. 357, No. 2, 427--437 (2009; Zbl 1190.34033) Full Text: DOI
Llibre, Jaume; Oliveira, Regilene D. S. Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3. (English) Zbl 1171.34035 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 10, 3549-3560 (2009); erratum ibid. 71, No. 12, 6378-6379 (2009). Reviewer: Gheorghe Tigan (Timisoara) MSC: 34C99 34C05 34C20 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{R. D. S. Oliveira}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 10, 3549--3560 (2009; Zbl 1171.34035) Full Text: DOI
Llibre, Jaume; Valls, Clàudia Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities. (English) Zbl 1176.34035 J. Differ. Equations 246, No. 6, 2192-2204 (2009). Reviewer: A. P. Sadovskii (Minsk) MSC: 34C05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, J. Differ. Equations 246, No. 6, 2192--2204 (2009; Zbl 1176.34035) Full Text: DOI
Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume Limit cycles near hyperbolas in quadratic systems. (English) Zbl 1169.34030 J. Differ. Equations 246, No. 1, 235-260 (2009). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34C07 34C05 34C37 34E15 PDFBibTeX XMLCite \textit{J. C. Artés} et al., J. Differ. Equations 246, No. 1, 235--260 (2009; Zbl 1169.34030) Full Text: DOI
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S. Structurally stable quadratic foliations. (English) Zbl 1170.34038 Rocky Mt. J. Math. 38, No. 2, 489-530 (2008). Reviewer: Sergei Yu. Pilyugin (St. Petersburg) MSC: 34D30 34-02 37E35 PDFBibTeX XMLCite \textit{X. Jarque} et al., Rocky Mt. J. Math. 38, No. 2, 489--530 (2008; Zbl 1170.34038) Full Text: DOI
Jiménez López, Víctor; Llibre, Jaume A topological characterization of the \(\omega \)-limit sets for analytic flows on the plane, the sphere and the projective plane. (English) Zbl 1134.37016 Adv. Math. 216, No. 2, 677-710 (2007). Reviewer: Ľubomír Snoha (Banská Bystrica) MSC: 37E35 37E30 37B20 37C10 54H20 PDFBibTeX XMLCite \textit{V. Jiménez López} and \textit{J. Llibre}, Adv. Math. 216, No. 2, 677--710 (2007; Zbl 1134.37016) Full Text: DOI
Cairó, Laurent; Llibre, Jaume Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2. (English) Zbl 1189.34065 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 2, 327-348 (2007). MSC: 34C05 34C14 34A05 PDFBibTeX XMLCite \textit{L. Cairó} and \textit{J. Llibre}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 2, 327--348 (2007; Zbl 1189.34065) Full Text: DOI
Giné, J.; Llibre, J. Integrability, degenerate centers, and limit cycles for a class of polynomial differential systems. (English) Zbl 1157.34022 Comput. Math. Appl. 51, No. 9-10, 1453-1462 (2006). Reviewer: Jinzhi Lei (Beijing) MSC: 34C05 34C07 34A05 PDFBibTeX XMLCite \textit{J. Giné} and \textit{J. Llibre}, Comput. Math. Appl. 51, No. 9--10, 1453--1462 (2006; Zbl 1157.34022) Full Text: DOI
Llibre, Jaume; Pessoa, Claudio Invariant circles for homogeneous polynomial vector fields on the 2-dimensional sphere. (English) Zbl 1150.37003 Rend. Circ. Mat. Palermo (2) 55, No. 1, 63-81 (2006). Reviewer: Armengol Gasull (Barcelona) MSC: 37C10 34C07 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Pessoa}, Rend. Circ. Mat. Palermo (2) 55, No. 1, 63--81 (2006; Zbl 1150.37003) Full Text: DOI
García, Belén; Llibre, Jaume; Pérez del Río, Jesús S. Phase portaits of the quadratic vector fields with a polynominal first integral. (English) Zbl 1150.34008 Rend. Circ. Mat. Palermo (2) 55, No. 3, 420-440 (2006). Reviewer: Alexander Grin (Grodno) MSC: 34C05 34C41 34A05 34C07 PDFBibTeX XMLCite \textit{B. García} et al., Rend. Circ. Mat. Palermo (2) 55, No. 3, 420--440 (2006; Zbl 1150.34008) Full Text: DOI
Giacomini, Hector; Giné, Jaume; Llibre, Jaume The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems. (English) Zbl 1111.34026 J. Differ. Equations 227, No. 2, 406-426 (2006). Reviewer: Armengol Gasull (Barcelona) MSC: 34C05 37C10 34C25 PDFBibTeX XMLCite \textit{H. Giacomini} et al., J. Differ. Equations 227, No. 2, 406--426 (2006; Zbl 1111.34026) Full Text: DOI arXiv
Jiang, Qibao; Llibre, Jaume Qualitative classification of singular points. (English) Zbl 1131.34304 Qual. Theory Dyn. Syst. 6, No. 1, 87-167 (2005). Reviewer: Iliya Iliev (Sofia) MSC: 34C05 37C15 34C41 PDFBibTeX XMLCite \textit{Q. Jiang} and \textit{J. Llibre}, Qual. Theory Dyn. Syst. 6, No. 1, 87--167 (2005; Zbl 1131.34304) Full Text: DOI
Llibre, Jaume; Medrado, João Carlos Darboux integrability and reversible quadratic vector fields. (English) Zbl 1107.34032 Rocky Mt. J. Math. 35, No. 6, 1999-2057 (2005). Reviewer: Yaping Liu (Pittsburg) MSC: 34C14 34A05 34C41 37C80 37C10 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{J. C. Medrado}, Rocky Mt. J. Math. 35, No. 6, 1999--2057 (2005; Zbl 1107.34032) Full Text: DOI
Chamberland, Marc; Llibre, Jaume; Świrszcz, Grzegorz Weakened Markus–Yamabe conditions for 2-dimensional global asymptotic stability. (English) Zbl 1081.34048 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 59, No. 6, 951-958 (2004). Reviewer: Dieter Erle (Dortmund) MSC: 34D23 PDFBibTeX XMLCite \textit{M. Chamberland} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 59, No. 6, 951--958 (2004; Zbl 1081.34048) Full Text: DOI
Llibre, Jaume; Zhang, Xiang Polynomial first integrals of quadratic systems. (English) Zbl 1041.34018 Rocky Mt. J. Math. 31, No. 4, 1317-1371 (2001). Reviewer: Alexander Grin (Grodno) MSC: 34C05 34A05 34C14 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, Rocky Mt. J. Math. 31, No. 4, 1317--1371 (2001; Zbl 1041.34018) Full Text: DOI Link
Llibre, Jaume; Ponce, Enrique Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields. (English) Zbl 1049.34052 Nonlinear Anal., Theory Methods Appl. 36, No. 5, B, 623-653 (1999). MSC: 34C23 34C25 37G15 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{E. Ponce}, Nonlinear Anal., Theory Methods Appl. 36, No. 5, 623--653 (1999; Zbl 1049.34052) Full Text: DOI