Similarities and differences between specification and non-uniform specification

Pub Date : 2024-04-15 DOI:10.1017/etds.2024.28
WANSHAN LIN, XUETING TIAN, CHENWEI YU
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Abstract

Pavlov [Adv. Math.295 (2016), 250–270; Nonlinearity32 (2019), 2441–2466] studied the measures of maximal entropy for dynamical systems with weak versions of specification property and found the existence of intrinsic ergodicity would be influenced by the assumptions of the gap functions. Inspired by these, in this article, we study the dynamical systems with non-uniform specification property. We give some basic properties these systems have and give an assumption for the gap functions to ensure the systems have the following five properties: CO-measures are dense in invariant measures; for every non-empty compact connected subset of invariant measures, its saturated set is dense in the total space; ergodic measures are residual in invariant measures; ergodic measures are connected; and entropy-dense. In addition, we will give examples to show the assumption is optimal.
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规范与非统一规范的异同
Pavlov[Adv. Math.295 (2016), 250-270; Nonlinearity32 (2019), 2441-2466]研究了具有弱版本规范属性的动力学系统的最大熵的度量,发现本征遍历性的存在会受到间隙函数假设的影响。受此启发,我们在本文中研究了具有非均匀规范性质的动力系统。我们给出了这些系统的一些基本性质,并给出了间隙函数的假设,以确保系统具有以下五个性质:CO度量在不变度量中是密集的;对于不变度量的每个非空紧凑连通子集,其饱和集在总空间中是密集的;遍历度量在不变度量中是残差的;遍历度量是连通的;熵密集。此外,我们还将举例说明该假设是最优的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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