{"title":"Morse – Smale Inequalities and Chafee – Infante Attractors","authors":"Leonardo Pires","doi":"10.1134/S156035472206003X","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we are concerned with the shape of the attractor <span>\\(\\mathcal{A}^{\\lambda}\\)</span> of the scalar Chafee – Infante equation. We construct a Morse – Smale vector field in the disk <span>\\(\\mathbb{D}^{k}\\)</span> topologically equivalent to\ninfinite-dimensional dynamics of the Chafee – Infante equation. As a consequence,\nwe obtain geometric properties of <span>\\(\\mathcal{A}^{\\lambda}\\)</span> using the Morse – Smale inequalities.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"27 6","pages":"629 - 646"},"PeriodicalIF":0.8000,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S156035472206003X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we are concerned with the shape of the attractor \(\mathcal{A}^{\lambda}\) of the scalar Chafee – Infante equation. We construct a Morse – Smale vector field in the disk \(\mathbb{D}^{k}\) topologically equivalent to
infinite-dimensional dynamics of the Chafee – Infante equation. As a consequence,
we obtain geometric properties of \(\mathcal{A}^{\lambda}\) using the Morse – Smale inequalities.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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