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Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities
1. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Catalonia, Spain |
2. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia |
References:
[1] |
A. Algaba and M. Reyes, Characterizing isochronous points and computing isochronous sections, J. Math. Anal. Appl., 355 (2009), 564-576.
doi: 10.1016/j.jmaa.2009.02.007. |
[2] |
J. Chavarriga and M. Sabatini, A survey of isochronous centers, Qualitative Theory of Dynamical Systems, 1 (1999), 1-70.
doi: 10.1007/BF02969404. |
[3] |
A. G. Choudhury and P. Guha, On commuting vector fields and Darboux functions for planar differential equations, Lobachevskii Journal of Mathematics, 34 (2013), 212-226.
doi: 10.1134/S1995080213030049. |
[4] |
R. Conti, Uniformly isochronous centers of polynomial systems in $\mathbbR^2$, Lecture Notes in Pure and Appl. Math., 152 (1994), 21-31. |
[5] |
F. Dumortier, J. Llibre and J. C. Artés, Qualitative Theory of Planar Differential Systems, Universitext, Spring-Verlag, 2006. |
[6] |
G. R. Fowles and G. L. Cassiday, Analytical Mechanics, Thomson Brooks/Cole, 2005. |
[7] |
E. A. González, Generic properties of polynomial vector fields at infinity, Trans. Amer. Math. Soc., 143 (1969), 201-222.
doi: 10.1090/S0002-9947-1969-0252788-8. |
[8] |
M. Han and V. G. Romanovski, Isochronicity and normal forms of polynomial systems of ODEs, J. Symb. Comput., 47 (2012), 1163-1174.
doi: 10.1016/j.jsc.2011.12.039. |
[9] |
J. Itikawa and J. Llibre, Phase portraits of uniform isochronous quartic centers, J. Comp. and Appl. Math., 287 (2015), 98-114.
doi: 10.1016/j.cam.2015.02.046. |
[10] |
W. S. Loud, Behavior of the period of solutions of certain plane autonomous systems near centers, Contributions to Diff. Eqs., 3 (1964), 21-36. |
[11] |
D. Neumann, Classification of continuous flows on 2-manifolds, Proc. Amer. Math. Soc., 48 (1975), 73-81.
doi: 10.1090/S0002-9939-1975-0356138-6. |
show all references
References:
[1] |
A. Algaba and M. Reyes, Characterizing isochronous points and computing isochronous sections, J. Math. Anal. Appl., 355 (2009), 564-576.
doi: 10.1016/j.jmaa.2009.02.007. |
[2] |
J. Chavarriga and M. Sabatini, A survey of isochronous centers, Qualitative Theory of Dynamical Systems, 1 (1999), 1-70.
doi: 10.1007/BF02969404. |
[3] |
A. G. Choudhury and P. Guha, On commuting vector fields and Darboux functions for planar differential equations, Lobachevskii Journal of Mathematics, 34 (2013), 212-226.
doi: 10.1134/S1995080213030049. |
[4] |
R. Conti, Uniformly isochronous centers of polynomial systems in $\mathbbR^2$, Lecture Notes in Pure and Appl. Math., 152 (1994), 21-31. |
[5] |
F. Dumortier, J. Llibre and J. C. Artés, Qualitative Theory of Planar Differential Systems, Universitext, Spring-Verlag, 2006. |
[6] |
G. R. Fowles and G. L. Cassiday, Analytical Mechanics, Thomson Brooks/Cole, 2005. |
[7] |
E. A. González, Generic properties of polynomial vector fields at infinity, Trans. Amer. Math. Soc., 143 (1969), 201-222.
doi: 10.1090/S0002-9947-1969-0252788-8. |
[8] |
M. Han and V. G. Romanovski, Isochronicity and normal forms of polynomial systems of ODEs, J. Symb. Comput., 47 (2012), 1163-1174.
doi: 10.1016/j.jsc.2011.12.039. |
[9] |
J. Itikawa and J. Llibre, Phase portraits of uniform isochronous quartic centers, J. Comp. and Appl. Math., 287 (2015), 98-114.
doi: 10.1016/j.cam.2015.02.046. |
[10] |
W. S. Loud, Behavior of the period of solutions of certain plane autonomous systems near centers, Contributions to Diff. Eqs., 3 (1964), 21-36. |
[11] |
D. Neumann, Classification of continuous flows on 2-manifolds, Proc. Amer. Math. Soc., 48 (1975), 73-81.
doi: 10.1090/S0002-9939-1975-0356138-6. |
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