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A minimal distal map on the torus with sub-exponential measure complexity

Published online by Cambridge University Press:  10 August 2018

WEN HUANG ,
LEIYE XU  and
XIANGDONG YE
WEN HUANG
Affiliation:
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China email wenh@mail.ustc.edu.cn, leoasa@mail.ustc.edu.cn, yexd@ustc.edu.cn
LEIYE XU
Affiliation:
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China email wenh@mail.ustc.edu.cn, leoasa@mail.ustc.edu.cn, yexd@ustc.edu.cn
XIANGDONG YE
Affiliation:
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China email wenh@mail.ustc.edu.cn, leoasa@mail.ustc.edu.cn, yexd@ustc.edu.cn
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Abstract

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In this paper the notion of sub-exponential measure complexity for an invariant Borel probability measure of a topological dynamical system is introduced. Then a minimal distal skew product map on the torus with sub-exponential measure complexity is constructed.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 4 , April 2020 , pp. 953 - 974
Copyright
© Cambridge University Press, 2018

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