Topological entropy of nonautonomous dynamical systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Liu, Kairan¹  Qiao, Yixiao²  Xu, Leiye¹ 

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

关键词: Entropy;    Nonautonomous dynamical system;    Induced system;    Finite-to-one extension;   

DOI  :  10.1016/j.jde.2019.11.029

来源: Elsevier

【 摘 要 】

Let M (X) be the space of all Borel probability measures on a compact metric space X endowed with the weak*-topology. In this paper, we prove that if the topological entropy of a nonautonomous dynamical system (X, {f(n)}(n=1)(+infinity)) vanishes, then so does that of its induced system (M(X), {f(n)}(n=1)(+infinity)) moreover, once the topological entropy of (X, {f(n)}(n=1)(+infinity)) is positive, that of its induced system (M(X), {f(n)}(n=1)(+infinity)) jumps to infinity. In contrast to Bowen's inequality, we construct a nonautonomous dynamical system whose topological entropy is not preserved under a finite-to-one extension. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free