Inverse limits, entropy and weak isomorphism for discrete dynamical systems

Author:

Brown James R.

Abstract

A categorical approach is taken to the study of a single measure-preserving transformation of a finite measure space and to inverse systems and inverse limits of such transformations. The questions of existence and uniqueness of inverse limits are settled. Sinaǐ’s theorem on generators is recast and slightly extended to say that entropy respects inverse limits, and various known results about entropy are obtained as immediate corollaries, e.g. systems with quasi-discrete or quasi-periodic spectrum have zero entropy. The inverse limit Φ \Phi of an inverse system { Φ α : α J } \{ {\Phi _\alpha }:\alpha \in J\} of dynamical systems is (1) ergodic, (2) weakly mixing, (3) mixing (of any order) iff each Φ α {\Phi _\alpha } has the same property. Finally, inverse limits are used to lift a weak isomorphism of dynamical systems Φ 1 {\Phi _1} and Φ 2 {\Phi _2} to an isomorphism of systems Φ ^ 1 {\hat \Phi _1} and Φ ^ 2 {\hat \Phi _2} with the same entropy.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference14 articles.

1. Metric automorphisms with quasi-discrete spectrum;Abramov, L. M.;Izv. Akad. Nauk SSSR Ser. Mat.,1962

2. A universal model for dynamical systems with quasi-discrete spectrum;Brown, James R.;Bull. Amer. Math. Soc.,1969

3. Inverse limits of measure spaces;Choksi, J. R.;Proc. London Math. Soc. (3),1958

4. Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation;Furstenberg, Harry;Math. Systems Theory,1967

Cited by 15 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Parameterized family of annular homeomorphisms with pseudo-circle attractors;Journal of Differential Equations;2024-10

2. Parametrized family of pseudo‐arc attractors: Physical measures and prime end rotations;Proceedings of the London Mathematical Society;2022-05-12

3. Digraph from power mapping on noncommutative groups;Journal of Algebra and Its Applications;2019-05-03

4. The topology and dynamics of the hyperspaces of normal fuzzy sets and their inverse limit spaces;Fuzzy Sets and Systems;2017-08

5. Dynamics of Endomorphism of Finite Abelian Groups;Discrete Dynamics in Nature and Society;2017

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3