Isochronicity and commutation of polynomial vector fields

Siberian Mathematical Journal

Volumn 40, Issue 1, 1999, Pages 23-38

  Volokitin, E P ^a   Ivanov, V V ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22644452165     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02674287     Document Type: Article

References (20)

1. V. V. Amel'kin, N. A. Lukashevich, and A. P. Sadovskiǐ, Nonlinear Oscillations in the Systems of Second Order [in Russian], Belorus. Univ., Minsk (1982).
2. P. Mardešić, C. Rousseau, and B. Toni, "Linearization of isochronous centers," J. Differential Equations, 121, No. 1, 67-108 (1995).
3. P. Mardešić, L. Moser-Jauslin, and C. Rousseau, "Darboux linearization and isochronous centers with a rational first integral," J. Differential Equations, 134, No. 2, 216-268 (1997).
4. M. Villarini, "Regularity properties of the period function near a center of a planar vector field," Nonlinear Anal., 19, No. 8, 787-803 (1992).
5. N. A. Lukashevich, "Isochronicity of a center for certain systems of differential equations," Differentsial'nye Uravneniya, 1, No. 5, 295-302 (1965).
6. V. I. Arnol'd, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1974).
7. M. Sabatini, "Characterizing isochronous centres by Lie brackets," Differential Equations Dynam. Systems, 5, No. 1, 91-99 (1997).
8. M. Sabatini, Quadratic Isochronous Centres Commute [Preprint, 461], Trento (1995).
9. C. J. Christopher and J. Devlin, "Isochronous centers in planar polynomial systems," SIAM J. Math. Anal., 28, No. 1, 162-177 (1997).
10. Mathematica. Version 2.2, Champaign, Illinois (1994). (Wolfram Research, Inc.)
11. E. Sáez and I. Szántó, "One-parameter family of a cubic Kolmogorov system with an isochronous center," Collect. Math., 48, No. 3, 297-301 (1997).
12. M. Sabatini, A Connection Between Isochronous Hamiltonian Centers and the Jacobian Conjecture [Preprint, No. 460], Trento (1995).
13. J. Devlin, "Coexisting isochronous and nonisochronous centres," Bull. London Math. Soc., 28, No. 134, 495-500 (1996).
14. J. Chavarriga and M. Sabatini, "A survey of isochronous centers," in: Winter School on Polynomial Vector Fields, 11-12 December, 1997, Lleida.
15. I. I. Pleshkan, "On isochronicity conditions of the system of two differential equations," Differentsial'nye Uravneniya, 4, No. 11, 1991-1993 (1968).
16. V. V. Amel'kin, "To the question on isochronicity of a center for two-dimensional analytic differential systems," Differentsial'nye Uravneniya, 13, No. 6, 971-980 (1977).
17. C. Chicone and M. Jacobs, "Bifurcation of critical periods for plane vector fields," Trans. Amer. Math. Soc., 312, No. 2, 433-486 (1989).
18. M. Sabatini, "On the period function of Liénard systems," J. Differential Equations (to appear).
19. 2," Differentsial'nye Uravneniya, 8, No. 8, 1435-1439 (1972).
20. N. A. Lukashevich, "Special Abel equations," Differentsial'nye Uravneniya, 34, No. 2, 282-284 (1998).