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1999 | 26 | 3 | 357-362
Tytuł artykułu

Quadratic Isochronous centers commute

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that every quadratic plane differential system having an isochronous center commutes with a polynomial differential system.
Rocznik
Tom
26
Numer
3
Strony
357-362
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-04-07
Twórcy
autor
  • Dipartimento di Matematica, Università di Trento, I-38050 Povo (TN), Italy
Bibliografia
  • [AFG] A. Algaba, E. Freire and E. Gamero, Isochronicity via normal form, preprint.
  • [C] R. Conti, Centers of polynomial systems in $R^2$, preprint, Firenze, 1990.
  • [CDL] C. J. Christopher, J. Devlin and N. G. Lloyd, On the classification of Liénard systems with amplitude-independent periods, preprint.
  • [CGG1] J. Chavarriga, J. Giné and I. García, Isochronous centers of cubic systems with degenerate infinity, Differential Equations Dynam. Systems 7 (1999), to appear.
  • [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.
  • [CGG3] J. Chavarriga, J. Giné and I. García, Isochronous centers of a linear center perturbed by fifth degree homogeneous polynomials, preprint, Univ. de Lleida.
  • [CJ] C. Chicone and M. Jacobs, Bifurcation of critical periods for plane vector fields, Trans. Amer. Math. Soc. 312 (1989), 433-486.
  • [D] J. Devlin, Coexisting isochronous and nonisochronous centers, Bull. Lond. Math. Soc. 28 (1996), 495-500.
  • [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.
  • [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.
  • [L] W. S. Loud, Behavior of the period of solutions of certain plane autonomous systems near centers, Contrib. Differential Equations 3 (1964), 21-36.
  • [MRT] P. Mardešić, C. Rousseau and B. Toni, Linearization of isochronous centers, J. Differential Equations 121 (1995), 67-108.
  • [MS] L. Mazzi and M. Sabatini, Commutators and linearizations of isochronous centers, preprint UTM 482, Univ. of Trento, 1996.
  • [NS] V. V. Nemytskiĭ and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton Univ. Press, Princeton, NJ, 1960.
  • [O] Z. Opial, Sur les périodes des solutions de l'équation différentielle x'' + g(x) = 0, Ann. Polon. Math. 10 (1961), 49-72.
  • [P] I. I. Pleshkan, A new method of investigating the isochronicity of a system of two differential equations, Differential Equations 5 (1969), 796-802.
  • [S1] M. Sabatini, On the period function of Liénard systems, J. Differential Equations 152 (1999), 467-487.
  • [S2] M. Sabatini, Quadratic isochronous centers commute, preprint UTM 461, Univ. of Trento, 1995.
  • [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.
  • [S4] M. Sabatini, Characterizing isochronous centers by Lie brackets, Differential Equations Dynam. Systems 5 (1997), 91-99.
  • [S5] M. Sabatini, Dynamics of commuting systems on two-dimensional manifolds, Ann. Mat. Pura Appl. (4) 173 (1997), 213-232.
  • [SC] G. Sansone e R. Conti, Equazioni differenziali non lineari, Cremonese, Roma, 1956.
  • [U] M. Urabe, Potential forces which yield periodic motions of a fixed period, J. Math. Mech. 10 (1961), 569-578.
  • [V] M. Villarini, Regularity properties of the period function near a center of a planar vector field, Nonlinear Anal. 19 (1992), 787-803.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv26i3p357bwm
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