Bifurcation from heteroclinic orbits with semi-hyperbolic equilibria
type: Item
instance of: scholarly article
title: Bifurcation from heteroclinic orbits with semi-hyperbolic equilibria
zbMATH Open document ID: 0813.34046
DOI: 10.1007/BF01765638
author: F. Battelli
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1995-01-15T00:00:00Z
review text: The author studies the problem of bifurcation from a heteroclinic orbit joining two semihyperbolic equilibria \(E_ 1\) and \(E_ 2\) in \(\mathbb{R}^ n\). The orbit is assumed to lie in the intersection of the unstable manifold of \(E_ 1\) and the stable manifold of \(E_ 2\). The author assumes that the equilibria undergo transcritical bifurcation when codimension one surfaces \(M_ 1\) and \(M_ 2\), respectively, in the parameter space \(\mathbb{R}^ k\) are crossed. He shows that there are Melnikov-type conditions that govern the existence of a heteroclinic orbit from an equilibrium near \(E_ 1\) to one near \(E_ 2\). The proofs use exponential trichotomies.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 711482
zbMATH Keywords: bifurcation from a heteroclinic orbit
zbMATH Keywords: Melnikov-type conditions
zbMATH Keywords: exponential trichotomies
reviewed by: Stephen Schecter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 711482