Some properties of coupled-expanding maps in compact sets

Zhang, Xu; Shi, Yuming; Chen, Guanrong

doi:10.1090/S0002-9939-2012-11339-5

Some properties of coupled-expanding maps in compact sets
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by Xu Zhang, Yuming Shi and Guanrong Chen

Proc. Amer. Math. Soc. 141 (2013), 585-595

DOI: https://doi.org/10.1090/S0002-9939-2012-11339-5

Published electronically: June 19, 2012

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Abstract:

In this paper, some properties of a strictly $A$-coupled-expanding map in compact subsets of a metric space are studied, where $A$ is a transition matrix. It is shown that this map has a compact invariant set on which it is topologically semi-conjugate to the subshift for $A$. If the subshift for $A$ has positive topological entropy, then the map is chaotic in the sense of Li-Yorke. Moreover, in the one-dimensional case, the map is at most two-to-one conjugate to the subshift for $A$ and chaotic in the sense of Devaney.

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