Bifurcations of rough heteroclinic loops with three saddle points
type: Item
instance of: scholarly article
title: Bifurcations of rough heteroclinic loops with three saddle points
zbMATH Open document ID: 1010.34037
author: Yinlai Jin
author: Deming Zhu
publication date: 2002-08-06T00:00:00Z
review text: The perturbed \(C^r\)-system \[ \dot z=f(z)+g(z,\mu)\tag{1} \] is considered with \(r\geq 4\), \(z\in \mathbb{R}^{m}\), \(\mu \in \mathbb{R}^k\), \(k\geq 3\), \(0\leq |\mu |\ll 1\), \(g(z,0)=0\). The unperturbed system (1) with \(\mu =0\) has a heteroclinic loop \(\Gamma \) connecting three hyperbolic critical points. Under certain transversal and nontwisted conditions, it is shown, for system (1) with \(\mu \neq 0\) small, the existence, uniqueness and incoexistence of heteroclinic loops with three or two saddle points along with homoclinic and periodic orbits near \(\Gamma\). The case with a heteroclinic loop in (1) connecting several hyperbolic critical points is also studied.
reviewed by: Michal Fečkan
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37C29
zbMATH DE Number: 1757459
zbMATH Keywords: local coordinates
zbMATH Keywords: heteroclinic loop
zbMATH Keywords: homoclinic orbit
zbMATH Keywords: periodic orbit
zbMATH Keywords: bifurcation surface
MaRDI profile type: Publication
full work available at URL: s101140100139
OpenAlex ID: W2019151760
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DOI: 10.1007/S101140100139
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1757459