{"title":"Rotational Entropy for Random Torus Maps","authors":"Weifeng Jiang, Zhengxing Lian, Yujun Zhu","doi":"10.1007/s10955-025-03443-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the rotational entropy <span>\\(h_r(\\varphi )\\)</span> is investigated for a random dynamical system <span>\\(\\varphi \\)</span> on the torus. The formula of <span>\\(h_r(\\varphi )\\)</span> is obtained for <span>\\(\\varphi \\)</span> which satisfies certain assumptions, and the lower and upper bounds of <span>\\(h_r(\\varphi )\\)</span> are given for more general <span>\\(\\varphi \\)</span>. Several examples are presented to show that these results may not hold without the assumptions. This work can be seen as a random version of the previous work (Jiang et al. in J Differ Equ 379:862–883, 2024), in which the rotational entropy was introduced and investigated as a homotopy invariant for any torus map.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10955-025-03443-8","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the rotational entropy \(h_r(\varphi )\) is investigated for a random dynamical system \(\varphi \) on the torus. The formula of \(h_r(\varphi )\) is obtained for \(\varphi \) which satisfies certain assumptions, and the lower and upper bounds of \(h_r(\varphi )\) are given for more general \(\varphi \). Several examples are presented to show that these results may not hold without the assumptions. This work can be seen as a random version of the previous work (Jiang et al. in J Differ Equ 379:862–883, 2024), in which the rotational entropy was introduced and investigated as a homotopy invariant for any torus map.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.