Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Anais da Academia Brasileira de Ciências

Jaume Llibre²  Marcelo Messias¹ 

[1] ,Universitat Autónoma de Barcelona Departament de Matemàtiques Barcelona Catalonia ,Spain

关键词: infinite heteroclinic loops;    periodic orbits;    symmetric systems;    ciclo heteroclínico infinito;    órbitas periódicas;    sistemas reversíveis;   

DOI  :  10.1590/S0001-37652007000400001

来源: SciELO

【 摘 要 】

In this paper we study a class of symmetric polynomial differential systems in R³, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity. The global study near infinity is performed using the Poincaré compactification. We prove that for all n Î N there is epsilonn > 0 such that for 0 < epsilon < epsilonn the system has at least n large amplitude periodic orbits bifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, one contained in the half-space y > 0 and the other in y < 0.

【 授权许可】

CC BY   
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