{"title":"关于动态系统阴影和局部熵特性的一些结果","authors":"","doi":"10.1007/s00574-024-00392-w","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give some necessary and sufficient conditions for (non) h-expansiveness under the assumption of shadowing and chain transitivity; and use the result to present a counter-example for a question raised by Artigue et al. (Proc Am Math Soc 150:3369–3378, 2022).</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Results on Shadowing and Local Entropy Properties of Dynamical Systems\",\"authors\":\"\",\"doi\":\"10.1007/s00574-024-00392-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give some necessary and sufficient conditions for (non) h-expansiveness under the assumption of shadowing and chain transitivity; and use the result to present a counter-example for a question raised by Artigue et al. (Proc Am Math Soc 150:3369–3378, 2022).</p>\",\"PeriodicalId\":501417,\"journal\":{\"name\":\"Bulletin of the Brazilian Mathematical Society, New Series\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Brazilian Mathematical Society, New Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00574-024-00392-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Brazilian Mathematical Society, New Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00574-024-00392-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
摘要 我们考虑了在阴影假设下动力系统的一些局部熵特性。在第一部分中，我们给出了可影点成为特定熵点的必要和充分条件。在第二部分中，我们给出了在阴影和链传递性假设下（非）h-扩展性的一些必要和充分条件；并利用该结果提出了一个反例，以回答 Artigue 等人提出的一个问题 (Proc Am Math Soc 150:3369-3378, 2022)。
Some Results on Shadowing and Local Entropy Properties of Dynamical Systems
Abstract
We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give some necessary and sufficient conditions for (non) h-expansiveness under the assumption of shadowing and chain transitivity; and use the result to present a counter-example for a question raised by Artigue et al. (Proc Am Math Soc 150:3369–3378, 2022).
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