A-coupled-expanding and distributional chaos

The concept of A-coupled-expanding map, which is one of the more natural and useful ideas generalized the horseshoe map, is well known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behaviour. In this paper, we focus the relati...

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Bibliographic Details
Published in:arXiv.org 2015-01
Main Authors: Kim, Cholsan, Ju, Hyonhui, Raith, Peter
Format: Article
Language:English
Online Access:Get full text
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Summary:The concept of A-coupled-expanding map, which is one of the more natural and useful ideas generalized the horseshoe map, is well known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behaviour. In this paper, we focus the relations between A-coupled-expanding and distributional chaos. We prove two theorems that give sufficient conditions for a strictly A-coupled-expanding map to be distributionally chaotic in the senses of two kinds, where A is an irreducible transition matrix.
ISSN:2331-8422
DOI:10.48550/arxiv.1401.2349