Chaos in forced impact systems
type: Item
instance of: scholarly article
title: Chaos in forced impact systems
zbMATH Open document ID: 1266.34074
author: F. Battelli
author: Michal Fečkan
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2013-03-14T00:00:00Z
review text: The aim of this paper is to develop a Melnikov method for showing chaos in a time-perturbed impact system whose unperturbed part has a piecewise continuous impact homoclinic orbit entering the discontinuity manifold in a transversal way. A Melnikov function is defined in such a way that the existence of a simple zero means that the system has impact solutions that behave chaotically in the sense of Smale. The time influence can be periodic or almost periodic and the system is allowed to have arbitrary finite dimension. The main result is illustrated using two concrete examples.
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37G20
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 6144754
zbMATH Keywords: Bernoulli shift
zbMATH Keywords: chaotic behavior
zbMATH Keywords: impact systems
MaRDI profile type: Publication
full work available at URL: dcdss.2013.6.861
OpenAlex ID: W2334949589
DOI: 10.3934/DCDSS.2013.6.861
description: scientific article; zbMATH DE number 6144754