Yang, Yantao; Zhang, Xiang A survey on local integrability and its regularity. (English) Zbl 07766586 Bul. Acad. Științe Repub. Mold., Mat. 2023, No. 1(101), 29-41 (2023). MSC: 34C05 34A34 PDFBibTeX XMLCite \textit{Y. Yang} and \textit{X. Zhang}, Bul. Acad. Științe Repub. Mold., Mat. 2023, No. 1(101), 29--41 (2023; Zbl 07766586) Full Text: DOI
Tian, Yuzhou Integrability analysis of Muthuswamy-Chua-Ginoux system. (English) Zbl 1497.37069 Physica D 434, Article ID 133212, 10 p. (2022). MSC: 37J35 70H06 94C05 PDFBibTeX XMLCite \textit{Y. Tian}, Physica D 434, Article ID 133212, 10 p. (2022; Zbl 1497.37069) Full Text: DOI
Li, Yongjun; Romanovski, Valery G. Isochronous solutions of a 3-dim symmetric quadratic system. (English) Zbl 1510.34092 Appl. Math. Comput. 405, Article ID 126250, 12 p. (2021). MSC: 34C45 34C25 37C27 PDFBibTeX XMLCite \textit{Y. Li} and \textit{V. G. Romanovski}, Appl. Math. Comput. 405, Article ID 126250, 12 p. (2021; Zbl 1510.34092) Full Text: DOI
Llibre, Jaume; Tian, Yuzhou A survey on the Kovalevskaya exponents and their applications. (English) Zbl 1482.34005 J. Math. Anal. Appl. 504, No. 2, Article ID 125576, 28 p. (2021). Reviewer: Huang Kaiyin (Singapur) MSC: 34A05 34D08 34M55 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{Y. Tian}, J. Math. Anal. Appl. 504, No. 2, Article ID 125576, 28 p. (2021; Zbl 1482.34005) Full Text: DOI
Aziz, Waleed; Christopher, Colin; Llibre, Jaume; Pantazi, Chara Three-dimensional Lotka-Volterra systems with 3:\(-1\):2-resonance. (English) Zbl 1476.34005 Mediterr. J. Math. 18, No. 4, Paper No. 167, 24 p. (2021). MSC: 34A05 34C20 34A34 34C14 PDFBibTeX XMLCite \textit{W. Aziz} et al., Mediterr. J. Math. 18, No. 4, Paper No. 167, 24 p. (2021; Zbl 1476.34005) Full Text: DOI
Aziz, Waleed; Amen, Azad; Pantazi, Chara Integrability and linearizability of a family of three-dimensional quadratic systems. (English) Zbl 1472.37060 Dyn. Syst. 36, No. 2, 317-331 (2021). MSC: 37J35 37J39 37C79 PDFBibTeX XMLCite \textit{W. Aziz} et al., Dyn. Syst. 36, No. 2, 317--331 (2021; Zbl 1472.37060) Full Text: DOI Link
Demina, Maria V.; Kuznetsov, Nikolai S. Liouvillian integrability and the Poincaré problem for nonlinear oscillators with quadratic damping and polynomial forces. (English) Zbl 1482.34003 J. Dyn. Control Syst. 27, No. 2, 403-415 (2021). Reviewer: Ioannis P. Stavroulakis (Ioannina) MSC: 34A05 34C15 34C45 PDFBibTeX XMLCite \textit{M. V. Demina} and \textit{N. S. Kuznetsov}, J. Dyn. Control Syst. 27, No. 2, 403--415 (2021; Zbl 1482.34003) Full Text: DOI
Giné, Jaume; Llibre, Jaume Formal Weierstrass nonintegrability criterion for some classes of polynomial differential systems in \(\mathbb{C}^2\). (English) Zbl 1446.34001 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 4, Article ID 2050064, 7 p. (2020). MSC: 34A05 PDFBibTeX XMLCite \textit{J. Giné} and \textit{J. Llibre}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 4, Article ID 2050064, 7 p. (2020; Zbl 1446.34001) Full Text: DOI
Li, YuQi; Chen, Yong The special class of second integrals of the KdV equation. (English) Zbl 1464.35301 Commun. Nonlinear Sci. Numer. Simul. 70, 193-202 (2019). MSC: 35Q53 34A05 PDFBibTeX XMLCite \textit{Y. Li} and \textit{Y. Chen}, Commun. Nonlinear Sci. Numer. Simul. 70, 193--202 (2019; Zbl 1464.35301) Full Text: DOI
Demina, Maria V. Invariant surfaces and Darboux integrability for non-autonomous dynamical systems in the plane. (English) Zbl 1411.70025 J. Phys. A, Math. Theor. 51, No. 50, Article ID 505202, 17 p. (2018). MSC: 70H06 70K40 PDFBibTeX XMLCite \textit{M. V. Demina}, J. Phys. A, Math. Theor. 51, No. 50, Article ID 505202, 17 p. (2018; Zbl 1411.70025) Full Text: DOI
Llibre, Jaume; Valls, Clàudia On the integrability of Hamiltonian systems with \(d\) degrees of freedom and homogenous polynomial potential of degree \(n\). (English) Zbl 1407.37095 Commun. Contemp. Math. 20, No. 8, Article ID 1750045, 9 p. (2018). MSC: 37J35 70H06 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Commun. Contemp. Math. 20, No. 8, Article ID 1750045, 9 p. (2018; Zbl 1407.37095) Full Text: DOI
Llibre, Jaume; Valls, Clàudia On the Darboux integrability of the Hindmarsh-Rose burster. (English) Zbl 1393.34042 Acta Math. Sin., Engl. Ser. 34, No. 6, 947-958 (2018). MSC: 34C05 34A34 34C14 34C45 34A05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Acta Math. Sin., Engl. Ser. 34, No. 6, 947--958 (2018; Zbl 1393.34042) Full Text: DOI
Llibre, Jaume; Oliveira, Regilene; Valls, Claudia On the Darboux integrability of a three-dimensional forced-damped differential system. (English) Zbl 1420.37040 J. Nonlinear Math. Phys. 24, No. 4, 473-494 (2017). MSC: 37J35 34C05 34A34 34C14 PDFBibTeX XMLCite \textit{J. Llibre} et al., J. Nonlinear Math. Phys. 24, No. 4, 473--494 (2017; Zbl 1420.37040) Full Text: DOI
Mahdi, Adam; Ferragut, Antoni; Valls, Claudia; Wiuf, Carsten Conservation laws in biochemical reaction networks. (English) Zbl 1387.37077 SIAM J. Appl. Dyn. Syst. 16, No. 4, 2213-2232 (2017). Reviewer: Gheorghe Tigan (Timisoara) MSC: 37N25 34C14 92C40 PDFBibTeX XMLCite \textit{A. Mahdi} et al., SIAM J. Appl. Dyn. Syst. 16, No. 4, 2213--2232 (2017; Zbl 1387.37077) Full Text: DOI
Llibre, Jaume; Valls, Clàudia On the Darboux integrability of the logarithmic galactic potentials. (English) Zbl 1417.37205 J. Geom. Phys. 121, 279-287 (2017). MSC: 37J35 37N05 85A05 70F15 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, J. Geom. Phys. 121, 279--287 (2017; Zbl 1417.37205) Full Text: DOI Link
Llibre, Jaume; Valls, Clàudia On the integrability of the 5-dimensional Lorenz system for the gravity-wave activity. (English) Zbl 1353.37120 Proc. Am. Math. Soc. 145, No. 2, 665-679 (2017). MSC: 37J35 37K10 34C05 34A34 34C14 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, Proc. Am. Math. Soc. 145, No. 2, 665--679 (2017; Zbl 1353.37120) Full Text: DOI Link
Llibre, Jaume; Valls, Claudia Darboux integrability of generalized Yang-Mills Hamiltonian system. (English) Zbl 1420.37037 J. Nonlinear Math. Phys. 23, No. 2, 234-242 (2016). MSC: 37J30 37J35 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, J. Nonlinear Math. Phys. 23, No. 2, 234--242 (2016; Zbl 1420.37037) Full Text: DOI
Llibre, Jaume; Valls, Claudia; Zhang, Xiang Liouvillian integrability versus Darboux polynomials. (English) Zbl 1364.34016 Qual. Theory Dyn. Syst. 15, No. 2, 503-515 (2016). MSC: 34A34 34C20 34C14 PDFBibTeX XMLCite \textit{J. Llibre} et al., Qual. Theory Dyn. Syst. 15, No. 2, 503--515 (2016; Zbl 1364.34016) Full Text: DOI Link
Zhang, Xiang Liouvillian integrability of polynomial differential systems. (English) Zbl 1331.34006 Trans. Am. Math. Soc. 368, No. 1, 607-620 (2016). Reviewer: Maite Grau (Lleida) MSC: 34A05 37C10 34C14 37G05 PDFBibTeX XMLCite \textit{X. Zhang}, Trans. Am. Math. Soc. 368, No. 1, 607--620 (2016; Zbl 1331.34006) Full Text: DOI arXiv
Llibre, Jaume; Valls, Claudia; Zhang, Xiang The completely integrable differential systems are essentially linear differential systems. (English) Zbl 1332.34004 J. Nonlinear Sci. 25, No. 4, 815-826 (2015). Reviewer: Marco Spadini (Firenze) MSC: 34A05 34C20 34C14 PDFBibTeX XMLCite \textit{J. Llibre} et al., J. Nonlinear Sci. 25, No. 4, 815--826 (2015; Zbl 1332.34004) Full Text: DOI Link
Chèze, Guillaume Darboux theory of integrability in the sparse case. (English) Zbl 1304.34002 J. Differ. Equations 257, No. 2, 601-609 (2014). Reviewer: Jaume Giné (Lleida) MSC: 34A05 34A34 34C14 13N15 PDFBibTeX XMLCite \textit{G. Chèze}, J. Differ. Equations 257, No. 2, 601--609 (2014; Zbl 1304.34002) Full Text: DOI arXiv
Llibre, Jaume; Valls, Claudia Darboux integrability of 2-dimensional Hamiltonian systems with homogenous potentials of degree 3. (English) Zbl 1286.70020 J. Math. Phys. 55, No. 3, 033507, 12 p. (2014). MSC: 70H05 70H06 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{C. Valls}, J. Math. Phys. 55, No. 3, 033507, 12 p. (2014; Zbl 1286.70020) Full Text: DOI Link
Llibre, Jaume; Walcher, Sebastian; Zhang, Xiang Local Darboux first integrals of analytic differential systems. (English) Zbl 1291.34068 Bull. Sci. Math. 138, No. 1, 71-88 (2014). Reviewer: Jaume Giné (Lleida) MSC: 34C20 34A05 34C05 34M99 PDFBibTeX XMLCite \textit{J. Llibre} et al., Bull. Sci. Math. 138, No. 1, 71--88 (2014; Zbl 1291.34068) Full Text: DOI
Buică, Adriana; García, Isaac A.; Maza, Susanna Inverse Jacobi multipliers: recent applications in dynamical systems. (English) Zbl 1348.37083 Ibáñez, Santiago (ed.) et al., Progress and challenges in dynamical systems. Proceedings of the international conference “Dynamical systems: 100 years after Poincaré”, Gijón, Spain, September 3–7, 2012. Berlin: Springer (ISBN 978-3-642-38829-3/hbk; 978-3-642-40137-4/ebook). Springer Proceedings in Mathematics & Statistics 54, 127-141 (2013). MSC: 37G15 37C10 37C60 37C27 34C23 37C80 PDFBibTeX XMLCite \textit{A. Buică} et al., Springer Proc. Math. Stat. 54, 127--141 (2013; Zbl 1348.37083) Full Text: DOI
Llibre, Jaume; Rebollo-Perdomo, Salomón Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in \(\mathbb R^3\). (English) Zbl 1300.34103 J. Dyn. Differ. Equations 25, No. 3, 777-793 (2013). Reviewer: Alessandro Calamai (Ancona) MSC: 34C40 34C05 37C10 34C45 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{S. Rebollo-Perdomo}, J. Dyn. Differ. Equations 25, No. 3, 777--793 (2013; Zbl 1300.34103) Full Text: DOI
Llibre, Jaume; Zhang, Xiang On the Darboux integrability of polynomial differential systems. (English) Zbl 1266.34002 Qual. Theory Dyn. Syst. 11, No. 1, 129-144 (2012). Reviewer: Maite Grau (Lleida) MSC: 34-02 34C14 34A05 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, Qual. Theory Dyn. Syst. 11, No. 1, 129--144 (2012; Zbl 1266.34002) Full Text: DOI Link
Cao, Jinlong; Jiang, Haixia Planar polynomial vector fields having first integrals and algebraic limit cycles. (English) Zbl 1191.34041 J. Math. Anal. Appl. 361, No. 1, 177-186 (2010). Reviewer: Valery Romanovski (Maribor) MSC: 34C07 34C05 34A05 PDFBibTeX XMLCite \textit{J. Cao} and \textit{H. Jiang}, J. Math. Anal. Appl. 361, No. 1, 177--186 (2010; Zbl 1191.34041) Full Text: DOI
Llibre, Jaume; Zhang, Xiang Darboux theory of integrability for polynomial vector fields in taking into account the multiplicity at infinity. (English) Zbl 1198.34054 Bull. Sci. Math. 133, No. 7, 765-778 (2009). Reviewer: Armengol Gasull (Barcelona) MSC: 34C14 34A34 34C05 37C10 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, Bull. Sci. Math. 133, No. 7, 765--778 (2009; Zbl 1198.34054) Full Text: DOI
Llibre, Jaume; Zhang, Xiang Darboux theory of integrability in \(\mathbb C^n\) taking into account the multiplicity. (English) Zbl 1163.34003 J. Differ. Equations 246, No. 2, 541-551 (2009). Reviewer: Alexey Remizov (Trieste) MSC: 34A05 34C14 34C45 34C07 PDFBibTeX XMLCite \textit{J. Llibre} and \textit{X. Zhang}, J. Differ. Equations 246, No. 2, 541--551 (2009; Zbl 1163.34003) Full Text: DOI
Dobrovol’skii, Viacheslav Alekseevich; Lokot’, Natalia Vasilevna; Strelcyn, Jean-Marie Mikhail Nikolaevich Lagutinskii (1871–1915): a misunderstood mathematician. (Mikhail Nikolaevich Lagutinskii (1871–1915) : un mathématicien méconnu.) (French) Zbl 0914.01023 Hist. Math. 25, No. 3, 245-264 (1998). MSC: 01A70 01A60 01A73 34-03 PDFBibTeX XMLCite \textit{V. A. Dobrovol'skii} et al., Hist. Math. 25, No. 3, 245--264 (1998; Zbl 0914.01023) Full Text: DOI