Quadratic Isochronous centers commute

 Access to full text

 Full (PDF)

1. [AFG] A. Algaba, E. Freire and E. Gamero, Isochronicity via normal form, preprint. Zbl1021.34022
2. [C] R. Conti, Centers of polynomial systems in $R^2$, preprint, Firenze, 1990. 
3. [CDL] C. J. Christopher, J. Devlin and N. G. Lloyd, On the classification of Liénard systems with amplitude-independent periods, preprint. 
4. [CGG1] J. Chavarriga, J. Giné and I. García, Isochronous centers of cubic systems with degenerate infinity, Differential Equations Dynam. Systems 7 (1999), to appear. Zbl0982.34025
5. [CGG2] J. Chavarriga, J. Giné and I. García, Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomials, Bull. Sci. Math. 123 (1999), 77-96. Zbl0921.34032
6. [CGG3] J. Chavarriga, J. Giné and I. García, Isochronous centers of a linear center perturbed by fifth degree homogeneous polynomials, preprint, Univ. de Lleida. Zbl0978.34028
7. [CJ] C. Chicone and M. Jacobs, Bifurcation of critical periods for plane vector fields, Trans. Amer. Math. Soc. 312 (1989), 433-486. Zbl0678.58027
8. [D] J. Devlin, Coexisting isochronous and nonisochronous centers, Bull. Lond. Math. Soc. 28 (1996), 495-500. Zbl0853.34032
9. [GGM1] A. Gasull, A. Guillamon and V. Mañosa, An explicit expression of the first Lyapunov and period constants with applications, J. Math. Anal. Appl. 211 (1997), 190-212. Zbl0882.34040
10. [GGM2] A. Gasull, A. Guillamon and V. Mañosa, Centre and isochronicity conditions for systems with homogeneous nonlinearities, in: Proc. 2nd Catalan Days on Appl. Math., Collect. Études, Presses Univ. Perpignan, Perpignan, 1995, 105-116. Zbl0909.34030
11. [L] W. S. Loud, Behavior of the period of solutions of certain plane autonomous systems near centers, Contrib. Differential Equations 3 (1964), 21-36. Zbl0139.04301
12. [MRT] P. Mardešić, C. Rousseau and B. Toni, Linearization of isochronous centers, J. Differential Equations 121 (1995), 67-108. Zbl0830.34023
13. [MS] L. Mazzi and M. Sabatini, Commutators and linearizations of isochronous centers, preprint UTM 482, Univ. of Trento, 1996. 
14. [NS] V. V. Nemytskiĭ and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton Univ. Press, Princeton, NJ, 1960. Zbl0089.29502
15. [O] Z. Opial, Sur les périodes des solutions de l'équation différentielle x'' + g(x) = 0, Ann. Polon. Math. 10 (1961), 49-72. Zbl0096.29604
16. [P] I. I. Pleshkan, A new method of investigating the isochronicity of a system of two differential equations, Differential Equations 5 (1969), 796-802. 
17. [S1] M. Sabatini, On the period function of Liénard systems, J. Differential Equations 152 (1999), 467-487. Zbl0922.34028
18. [S2] M. Sabatini, Quadratic isochronous centers commute, preprint UTM 461, Univ. of Trento, 1995. 
19. [S3] M. Sabatini, Qualitative analysis of commuting flows on two-dimensional manifolds, in: EQUADIFF 95-International Conf. on Differential Equations (Lisboã, 1995), L. Magalhaes, C. Rocha and L. Sanchez (eds.), World Sci., Singapore, 1998, 494-497. 
20. [S4] M. Sabatini, Characterizing isochronous centers by Lie brackets, Differential Equations Dynam. Systems 5 (1997), 91-99. 
21. [S5] M. Sabatini, Dynamics of commuting systems on two-dimensional manifolds, Ann. Mat. Pura Appl. (4) 173 (1997), 213-232. Zbl0941.34018
22. [SC] G. Sansone e R. Conti, Equazioni differenziali non lineari, Cremonese, Roma, 1956. Zbl0075.26803
23. [U] M. Urabe, Potential forces which yield periodic motions of a fixed period, J. Math. Mech. 10 (1961), 569-578. Zbl0100.29901
24. [V] M. Villarini, Regularity properties of the period function near a center of a planar vector field, Nonlinear Anal. 19 (1992), 787-803. Zbl0769.34033