Algaba, Antonio; García, Cristóbal; Reyes, Manuel; Giné, Jaume Analytically integrable system orbitally equivalent to a semi-quasihomogeneous system. (English) Zbl 1521.34003 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 234, Article ID 113304, 11 p. (2023). MSC: 34A05 34C20 34C05 PDFBibTeX XMLCite \textit{A. Algaba} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 234, Article ID 113304, 11 p. (2023; Zbl 1521.34003) Full Text: DOI
Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume Center problem for generic degenerate vector fields. (English) Zbl 1487.34088 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 214, Article ID 112597, 23 p. (2022). Reviewer: Valery A. Gaiko (Minsk) MSC: 34C05 34C25 PDFBibTeX XMLCite \textit{A. Algaba} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 214, Article ID 112597, 23 p. (2022; Zbl 1487.34088) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume A new normal form for monodromic nilpotent singularities of planar vector fields. (English) Zbl 1482.34106 Mediterr. J. Math. 18, No. 5, Paper No. 176, 18 p. (2021). Reviewer: Alexey O. Remizov (Moskva) MSC: 34C20 34C05 34C25 PDFBibTeX XMLCite \textit{A. Algaba} et al., Mediterr. J. Math. 18, No. 5, Paper No. 176, 18 p. (2021; Zbl 1482.34106) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Reyes, Manuel Analytically integrable centers of perturbations of cubic homogeneous systems. (English) Zbl 1472.34055 Qual. Theory Dyn. Syst. 20, No. 2, Paper No. 43, 17 p. (2021). Reviewer: Huang Kaiyin (Singapur) MSC: 34C05 34A05 34E10 34C14 PDFBibTeX XMLCite \textit{A. Algaba} et al., Qual. Theory Dyn. Syst. 20, No. 2, Paper No. 43, 17 p. (2021; Zbl 1472.34055) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume Orbitally universal centers. (English) Zbl 1511.34038 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 195, Article ID 111746, 10 p. (2020). MSC: 34C05 34C25 34C14 PDFBibTeX XMLCite \textit{A. Algaba} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 195, Article ID 111746, 10 p. (2020; Zbl 1511.34038) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume Center conditions of a particular polynomial differential system with a nilpotent singularity. (English) Zbl 1478.34031 J. Math. Anal. Appl. 483, No. 2, Article ID 123639, 12 p. (2020). Reviewer: Armengol Gasull (Barcelona) MSC: 34C05 34A05 34C14 PDFBibTeX XMLCite \textit{A. Algaba} et al., J. Math. Anal. Appl. 483, No. 2, Article ID 123639, 12 p. (2020; Zbl 1478.34031) Full Text: DOI
Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume Analytic integrability around a nilpotent singularity: the non-generic case. (English) Zbl 1483.34006 Commun. Pure Appl. Anal. 19, No. 1, 407-423 (2020). Reviewer: Valery Romanovski (Maribor) MSC: 34A05 34C05 34C14 PDFBibTeX XMLCite \textit{A. Algaba} et al., Commun. Pure Appl. Anal. 19, No. 1, 407--423 (2020; Zbl 1483.34006) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor. (English) Zbl 1464.34006 Commun. Nonlinear Sci. Numer. Simul. 71, 130-140 (2019). MSC: 34A05 34C05 PDFBibTeX XMLCite \textit{A. Algaba} et al., Commun. Nonlinear Sci. Numer. Simul. 71, 130--140 (2019; Zbl 1464.34006) Full Text: DOI Link
Algaba, Antonio; García, Cristóbal; Giné, Jaume Nondegenerate and nilpotent centers for a cubic system of differential equations. (English) Zbl 1416.34020 Qual. Theory Dyn. Syst. 18, No. 1, 333-345 (2019). MSC: 34C05 34A05 34C25 PDFBibTeX XMLCite \textit{A. Algaba} et al., Qual. Theory Dyn. Syst. 18, No. 1, 333--345 (2019; Zbl 1416.34020) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume Analytic integrability around a nilpotent singularity. (English) Zbl 1432.34002 J. Differ. Equations 267, No. 1, 443-467 (2019). Reviewer: Valery Romanovski (Maribor) MSC: 34A05 34C05 34C20 34C14 PDFBibTeX XMLCite \textit{A. Algaba} et al., J. Differ. Equations 267, No. 1, 443--467 (2019; Zbl 1432.34002) Full Text: DOI arXiv
Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields. (English) Zbl 1395.34047 J. Math. Anal. Appl. 466, No. 1, 183-198 (2018). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34C25 34C05 PDFBibTeX XMLCite \textit{A. Algaba} et al., J. Math. Anal. Appl. 466, No. 1, 183--198 (2018; Zbl 1395.34047) Full Text: DOI
Algaba, Antonio; Fuentes, Natalia; García, Cristóbal; Reyes, Manuel Algebraic inverse integrating factors for a class of generalized nilpotent systems. (English) Zbl 1411.34055 Ortegón Gallego, Francisco (ed.) et al., Trends in differential equations and applications. Selected papers based on the presentations at the XXIVth congress on differential equations and applications/XIVth congress on applied mathematics, Cádiz, Spain, June 8–12, 2015. Cham: Springer. SEMA SIMAI Springer Ser. 8, 287-300 (2016). Reviewer: Iliya Iliev (Sofia) MSC: 34C20 34A05 34C05 PDFBibTeX XMLCite \textit{A. Algaba} et al., SEMA SIMAI Springer Ser. 8, 287--300 (2016; Zbl 1411.34055) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume Nilpotent centres via inverse integrating factors. (English) Zbl 1384.34037 Eur. J. Appl. Math. 27, No. 5, 781-795 (2016). MSC: 34C05 34C20 34C25 PDFBibTeX XMLCite \textit{A. Algaba} et al., Eur. J. Appl. Math. 27, No. 5, 781--795 (2016; Zbl 1384.34037) Full Text: DOI
Algaba, Antonio; Checa, Isabel; García, Cristóbal; Giné, Jaume Analytic integrability inside a family of degenerate centers. (English) Zbl 1354.34005 Nonlinear Anal., Real World Appl. 31, 288-307 (2016). Reviewer: Iliya Iliev (Sofia) MSC: 34A05 34C20 34C05 34C14 PDFBibTeX XMLCite \textit{A. Algaba} et al., Nonlinear Anal., Real World Appl. 31, 288--307 (2016; Zbl 1354.34005) Full Text: DOI Link
Algaba, Antonio; García, Cristóbal; Giné, Jaume Analytic integrability of some examples of degenerate planar vector fields. (English) Zbl 1343.34003 Acta Appl. Math. 141, No. 1, 1-15 (2016). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34A05 34C05 34C20 PDFBibTeX XMLCite \textit{A. Algaba} et al., Acta Appl. Math. 141, No. 1, 1--15 (2016; Zbl 1343.34003) Full Text: DOI Link
Algaba, Antonio; Checa, Isabel; García, Cristóbal; Reyes, Manuel Local phase portraits through the Newton diagram of a vector field. (English) Zbl 1330.34047 Acta Math. Sin., Engl. Ser. 31, No. 6, 1015-1034 (2015). Reviewer: Alexey O. Remizov (São Carlos) MSC: 34C05 34M35 34C20 PDFBibTeX XMLCite \textit{A. Algaba} et al., Acta Math. Sin., Engl. Ser. 31, No. 6, 1015--1034 (2015; Zbl 1330.34047) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume Analytic integrability for some degenerate planar vector fields. (English) Zbl 1306.34046 J. Differ. Equations 257, No. 2, 549-565 (2014). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34C05 37G15 34A05 34C20 PDFBibTeX XMLCite \textit{A. Algaba} et al., J. Differ. Equations 257, No. 2, 549--565 (2014; Zbl 1306.34046) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume On the formal integrability problem for planar differential systems. (English) Zbl 1282.34005 Abstr. Appl. Anal. 2013, Article ID 482305, 10 p. (2013). Reviewer: M. A. M. Alwash (Culver City) MSC: 34A05 34C05 34C25 34C45 PDFBibTeX XMLCite \textit{A. Algaba} et al., Abstr. Appl. Anal. 2013, Article ID 482305, 10 p. (2013; Zbl 1282.34005) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Giné, Jaume Analytic integrability for some degenerate planar systems. (English) Zbl 1278.34001 Commun. Pure Appl. Anal. 12, No. 6, 2797-2809 (2013). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34A05 34C05 34C20 PDFBibTeX XMLCite \textit{A. Algaba} et al., Commun. Pure Appl. Anal. 12, No. 6, 2797--2809 (2013; Zbl 1278.34001) Full Text: DOI
Algaba, A.; García, C.; Reyes, M. A note on analytic integrability of planar vector fields. (English) Zbl 1268.34003 Eur. J. Appl. Math. 23, No. 5, 555-562 (2012). Reviewer: Jaume Giné (Lleida) MSC: 34A05 34C05 PDFBibTeX XMLCite \textit{A. Algaba} et al., Eur. J. Appl. Math. 23, No. 5, 555--562 (2012; Zbl 1268.34003) Full Text: DOI
Algaba, Antonio; García, Cristóbal; Reyes, Manuel Nilpotent systems admitting an algebraic inverse integrating factor over \(\mathbb{C}((x,y))\). (English) Zbl 1267.34002 Qual. Theory Dyn. Syst. 10, No. 2, 303-316 (2011). Reviewer: Jaume Giné (Lleida) MSC: 34A05 34C05 34C07 PDFBibTeX XMLCite \textit{A. Algaba} et al., Qual. Theory Dyn. Syst. 10, No. 2, 303--316 (2011; Zbl 1267.34002) Full Text: DOI
Algaba, A.; García, C.; Reyes, M. Characterization of a monodromic singular point of a planar vector field. (English) Zbl 1226.34031 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 16, 5402-5414 (2011). Reviewer: Valery A. Gaiko (Groningen) MSC: 34C05 34C25 PDFBibTeX XMLCite \textit{A. Algaba} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 16, 5402--5414 (2011; Zbl 1226.34031) Full Text: DOI
Algaba, A.; García, C.; Reyes, M. Rational integrability of two-dimensional quasi-homogeneous polynomial differential systems. (English) Zbl 1201.34050 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 5, 1318-1327 (2010). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34C05 34A05 PDFBibTeX XMLCite \textit{A. Algaba} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 5, 1318--1327 (2010; Zbl 1201.34050) Full Text: DOI
Algaba, A.; García, C.; Reyes, M. Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations. (English) Zbl 1201.34061 Appl. Math. Comput. 215, No. 1, 314-323 (2009). Reviewer: Armengol Gasull (Barcelona) MSC: 34C23 34C25 34C07 37C10 34C05 PDFBibTeX XMLCite \textit{A. Algaba} et al., Appl. Math. Comput. 215, No. 1, 314--323 (2009; Zbl 1201.34061) Full Text: DOI
Algaba, A.; Gamero, E.; García, C. The integrability problem for a class of planar systems. (English) Zbl 1165.34023 Nonlinearity 22, No. 2, 395-420 (2009). Reviewer: Alexey Remizov (Trieste) MSC: 34C20 34C05 34A05 PDFBibTeX XMLCite \textit{A. Algaba} et al., Nonlinearity 22, No. 2, 395--420 (2009; Zbl 1165.34023) Full Text: DOI
Algaba, A.; García, C.; Reyes, M. The center problem for a family of systems of differential equations having a nilpotent singular point. (English) Zbl 1156.34031 J. Math. Anal. Appl. 340, No. 1, 32-43 (2008). Reviewer: Armengol Gasull (Barcelona) MSC: 34C25 37C27 34C05 PDFBibTeX XMLCite \textit{A. Algaba} et al., J. Math. Anal. Appl. 340, No. 1, 32--43 (2008; Zbl 1156.34031) Full Text: DOI