截面双曲流的熵理论

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-01 DOI:10.1016/j.anihpc.2020.10.001

Maria José Pacifico , Fan Yang , Jiagang Yang

{"title":"截面双曲流的熵理论","authors":"Maria José Pacifico , Fan Yang , Jiagang Yang","doi":"10.1016/j.anihpc.2020.10.001","DOIUrl":null,"url":null,"abstract":"<div>We use entropy theory as a new tool to study sectional hyperbolic flows in any dimension. We show that for <math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math> flows, every sectional hyperbolic set Λ is entropy expansive, and the topological entropy varies continuously with the flow. Furthermore, if Λ is Lyapunov stable, then it has positive entropy; in addition, if Λ is a chain recurrent class, then it contains a periodic orbit. As a corollary, we prove that for <math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math> generic flows, every Lorenz-like class is an attractor.</div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.10.001","citationCount":"20","resultStr":"{\"title\":\"Entropy theory for sectional hyperbolic flows\",\"authors\":\"Maria José Pacifico , Fan Yang , Jiagang Yang\",\"doi\":\"10.1016/j.anihpc.2020.10.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We use entropy theory as a new tool to study sectional hyperbolic flows in any dimension. We show that for <math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math> flows, every sectional hyperbolic set Λ is entropy expansive, and the topological entropy varies continuously with the flow. Furthermore, if Λ is Lyapunov stable, then it has positive entropy; in addition, if Λ is a chain recurrent class, then it contains a periodic orbit. As a corollary, we prove that for <math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math> generic flows, every Lorenz-like class is an attractor.</div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2021-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.10.001\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0294144920300962\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0294144920300962","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 20

摘要

我们将熵理论作为一种新的工具来研究任意维度的截面双曲流。我们证明了对于C1流，每个截面双曲集Λ都是熵膨胀的，并且拓扑熵随流连续变化。更进一步，如果Λ是李雅普诺夫稳定的，则它具有正熵;另外，如果Λ是一个链循环类，那么它包含一个周期轨道。作为推论，我们证明了对于C1泛型流，每个类洛伦兹类都是吸引子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Entropy theory for sectional hyperbolic flows

We use entropy theory as a new tool to study sectional hyperbolic flows in any dimension. We show that for $C^{1}$ flows, every sectional hyperbolic set Λ is entropy expansive, and the topological entropy varies continuously with the flow. Furthermore, if Λ is Lyapunov stable, then it has positive entropy; in addition, if Λ is a chain recurrent class, then it contains a periodic orbit. As a corollary, we prove that for $C^{1}$ generic flows, every Lorenz-like class is an attractor.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.