Invariant algebraic curves for the cubic Liénard system with linear damping

Bulletin des Sciences Mathématiques - Tập 130 - Trang 428-441 - 2006
J. Chavarriga1, I.A. García1, J. Llibre2, H. Żołądek3
1Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Spain
2Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
3Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

Tài liệu tham khảo

Arnold, 1992 Arnold, 1982 Arnold, 1985, Singularities of Differentiable Maps: vol. I. The Classification of Critical Points, Caustics and Wave Fronts, vol. 82 Chavarriga, 1999, Darboux integrability and the inverse integrating factor, J. Differential Equations, 157, 163, 10.1006/jdeq.1998.3621 Chavarriga, 2005, Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems, Bull. Sci. Math., 129, 99, 10.1016/j.bulsci.2004.09.002 Dumortier, 1996, On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations, Nonlinearity, 9, 1489, 10.1088/0951-7715/9/6/006 Dumortier, 1990, Cubic Liénard equations with linear damping, Nonlinearity, 3, 1015, 10.1088/0951-7715/3/4/004 Hayashi, 1996, On polynomial Liénard systems which have invariant algebraic curves, Funkcial. Ekvac., 39, 403 J. Llibre, G. Świrszcz, An example of a cubic Liénard system with linear damping having invariant algebraic curves of arbitrary degree, Preprint, CRM, 2003 Odani, 1995, The limit cycle of the van der Pol equation is not algebraic, J. Differential Equations, 115, 146, 10.1006/jdeq.1995.1008 Ye Yangian, 1986, Theory of Limit Cycles, vol. 66 Żołądek, 1998, Algebraic invariant curves for the Liénard equation, Trans. Amer. Math. Soc., 350, 1681, 10.1090/S0002-9947-98-02002-9