Chaos induced by heteroclinic cycles connecting repellers and saddles in locally compact metric spaces
type: Item
instance of: scholarly article
title: Chaos induced by heteroclinic cycles connecting repellers and saddles in locally compact metric spaces
zbMATH Open document ID: 1171.37018
author: Zong-cheng Li
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-06-24T00:00:00Z
review text: From the abstract: This paper is concerned with chaos induced by heteroclinic cycles, connecting repellers and saddles for maps in locally compact metric spaces [cf. \textit{Z. Li, Y. Shi} and \textit{C. Zhang}, Chaos Solitons Fractals 36, No. 3, 746--761 (2008; Zbl 1142.37014)]. In this paper, one criterion of chaos for such types of maps, is established in locally compact metric spaces, by employing the coupled-expansion theory, where the map is only continuous in some domains of interest. In particular, one criterion of chaos in the Euclidean space \(\mathbb R^n\) is also established. The maps in the criteria are proved to have a positive topological entropy and to be chaotic in the sense of Li-Yorke. An illustrative example is provided with computer simulations.
reviewed by: Kazuhiro Sakai
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37D20
zbMATH DE Number: 5569429
zbMATH Keywords: chaos in the sense of Li-York
zbMATH Keywords: heteroclinic cycles connecting repellers and saddles
zbMATH Keywords: coupled-expansion theory
zbMATH Keywords: locally compact metric spaces
MaRDI profile type: Publication
full work available at URL: j.na.2008.11.097
OpenAlex ID: W2065945434
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DOI: 10.1016/J.NA.2008.11.097
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description: scientific article; zbMATH DE number 5569429