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arXiv · 1401.2349

A-coupled-expanding and distributional chaos

Cholsan Kim·Hyonhui Ju·Peter Raith
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Abstract

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.

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Cholsan Kim, Hyonhui Ju, Peter Raith. 2014-01-09. A-coupled-expanding and distributional chaos. https://doi.org/10.1016/j.chaos.2015.06.010

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