Mean dimension of shifts of finite type and of generalized inverse limits

Kazuhiro Kawamura

doi:10.3934/dcds.2020200

Article Contents

2020, Volume 40, Issue 8: 4767-4775. Doi: 10.3934/dcds.2020200

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Mean dimension of shifts of finite type and of generalized inverse limits

Kazuhiro Kawamura

Department of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan

Received: June 2019

Revised: December 2019

Published: May 2020

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Abstract

We study mean dimension of shifts of finite type defined on compact metric spaces and give its lower bound when the shift possesses a certain "periodic block" of arbitrarily large length. The result is applied to shift maps on generalized inverse limits with upper semi-continuous closed set-valued functions. In particular we obtain a refinement of some results due to Banič [1] and Erceg and Kennedy [5] on the dimension of the inverse limit spaces and topological entropy of their shifts.

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Mathematics Subject Classification: Primary: 37B40, 37C25; Secondary: 54C60, 54H20.

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References

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