Characterization of isochronous foci for planar analytic differential systems

Royal Society of Edinburgh - Proceedings A

Volumn 135, Issue 5, 2005, Pages 985-998

  Giné, Jaume ^a   Grau, Maite ^a  

^a UNIVERSITY OF LLEIDA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29144484617     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500004236     Document Type: Conference Paper

References (18)

1. A. Algaba, E. Freire and E. Gamero. Isochronicity via normal form. Qual. Theory Dyn. Syst. 1 (2000), 133-156.
2. A. A. Andronov, E. A. Leontovich, I. I. Gordon and A. G. Maǐer. Qualitative theory of second-order dynamic systems (Engl. transi. D. Louvish.) (New York: Halsted Press; Jerusalem: Israel Program for Scientific Translations, 1973).
3. J. Chavarriga and M. Sabatini. A survey of isochronous centers. Qual. Theory Dynam. Syst. 1 (1999), 1-70.
4. J. Chavarriga, I. A. García and J. Giné. On Lie's symmetries for planar polynomial differential systems. Nonlinearity 14 (2001), 863-880.
5. S. N. Chow, C. Li and D. Wang. Normal forms and bifurcation of planar vector fields (Cambrige University Press, 1994).
6. 2. Lecture Notes in Pure and Applied Mathematics, vol. 152, pp. 21-31 (New York: Dekker, 1994).
7. E. Freire, A. Gasull and A. Guillamon. A characterization of isochronous centres in terms of symmetries. Rev. Mat. Iber. 20 (2004), 205-222.
8. A. Gasull, A. Guillamon and J. Villadelprat. The period function for second-order quadratic ODEs is monotone. Qual. Theory Dynam. Syst. 4 (2004), 329-352.
9. J. Giné. Isochronous foci for analytic differential systems, Int. J. Bifurcation Chaos 13 (2003), 1-7.
10. P. J. Olver. Applications of Lie groups to differential equations, 2nd edn. Graduate Texts in Mathematics, vol. 107 (Springer, 1993).
11. L. Perko. Differential equations and dynamical systems, 3rd edn. Texts in Applied Mathematics, vol. 7 (Springer, 2001).
12. H. Poincaré. Thesis, 1879 (Paris: Gauthier Villars, 1928).
13. H. Poincaré. Oeuvres I, pp. 59-129 (Paris: Gauthier Villars, 1928).
14. M. Sabatini. Characterizing isochronous centres by Lie brackets. Diff. Eqns Dynam. Systems 5 (1997), 91-99.
15. M. Sabatini. Dynamics of commuting systems on two-dimensional manifolds. Annli Mat. Pura Appl. 173 (1997), 213-232.
16. M. Sabatini. Nonperiodic isochronous oscillations in plane differential systems. Annli Mat. Pura Appl. 182 (2003), 487-501.
17. M. Villarini. Regularity properties of the period function near a center of a planar vector field. Nonlin. Analysis 19 (1992), 787-803.
18. Z. Zhang, T. Ding, W. Huang and Z. Dong. Qualitative theory of differential equations. Translations of Mathematical Monographs, vol. 101 (Providence, RI: American Mathematical Society, 1992).