周期扰动下分离指标对异宿轨道分支的影响

Abstract

Abstract:

By using the method of Lyapunov-Schmidt reduction and exponential dichotomies, we consider the degenerate heteroclinic orbit bifurcation with $m$ dimensional periodic perturbations. The variational equation along the heteroclinic orbit has $d (d\ge1)$ bounded solutions. The splitting index of the unperturbed heteroclinic orbit is $s$. The bifurcation equation has $d+m$ variables and $d-s$ equations. The zeros of bifurcation function correspond to the existence of heteroclinic orbits for perturbed equation. If the splitting index $s<0$, it needs at least $1-s$ dimensional periodic perturbation can break the unperturbed heteroclinic orbit. If the splitting index $s\geq0$, there is a small perturbation can break the unperturbed heteroclinic orbit.

Key words: Degenerate heteroclinic bifurcation, Lyapunov-Schmidt reduction, Exponential dichotomy

CLC Number:

O175.1

Bin Long,Shanshan Xu,Hui Cao,Jianquan Li. The Influence of Splitting Index on Heteroclinic Orbit Bifurcation Under Periodic Perturbation[J].Acta mathematica scientia,Series A, 2021, 41(5): 1516-1528.

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The Influence of Splitting Index on Heteroclinic Orbit Bifurcation Under Periodic Perturbation

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