Discrete dichotomies and bifurcations from critical homoclinic orbits
type: Item
instance of: scholarly article
title: Discrete dichotomies and bifurcations from critical homoclinic orbits
zbMATH Open document ID: 0959.37041
author: F. Battelli
author: Claudio Lazzari
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-04-24T00:00:00Z
review text: The authors consider discrete time dynamical systems of the form \(x_{n+1} = f(x_n) + \mu g(x_n,\mu)\) with \(x \in \mathbb R^n\). The unperturbed map for \(\mu= 0\) has an orbit \(\{ \gamma_n \}\) homoclinic to a hyperbolic fixed point \(p\). Moreover, at one point \(\gamma_0\) in the orbit, \(Df (\gamma_0)\) is not invertible. Bifurcation equations for homoclinic orbits that are close to \(\{ \gamma_n\}\) if \(\mu\) is small are derived.
reviewed by: Ale Jan Homburg
Mathematics Subject Classification ID: 37G20
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 1215732
zbMATH Keywords: discrete time dynamical systems
zbMATH Keywords: bifurcation
zbMATH Keywords: homoclinic orbits
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5769
OpenAlex ID: W2048139228
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DOI: 10.1006/JMAA.1997.5769
description: scientific article; zbMATH DE number 1215732