On manifolds of connecting orbits in discretizations of dynamical systems
type: Item
instance of: scholarly article
title: On manifolds of connecting orbits in discretizations of dynamical systems
zbMATH Open document ID: 1018.37018
DOI: 10.1016/S0362-546X(02)00269-9
author: Wolf-Jürgen Beyn
author: Yongkui Zou
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: Time discretizations of continuous dynamical systems lead often to subtlephenomena near homoclinic and heteroclinic orbits. A fundamental result of this type was derived by \textit{B. Fiedler} and \textit{J. Scheurle} [Mem. Amer. Math. Soc. 570 (1996; Zbl 0923.34049)]. The authors provide an alternative approach, recover and generalize these results. They show that one-step methods, when applied to a one-parameter dynamical systems with a homoclinic orbit, exhibit a closed loop of discrete homoclinic orbits. On this loop the parameter varies periodically while the orbit shifts its index after one revolution. At least two homoclinic tangencies occur. This approach is suitable to systems with finite smoothness and general connecting orbits.
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 65P30
zbMATH DE Number: 1880108
zbMATH Keywords: dynamical systems
zbMATH Keywords: one-step methods
zbMATH Keywords: connecting orbits
zbMATH Keywords: homoclinic tangencies
zbMATH Keywords: time discretization
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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full work available at URL: s0362-546x(02)00269-9
OpenAlex ID: W2093427279
description: scientific article; zbMATH DE number 1880108