{"title":"Multi-Dimensional Hyperbolic Chaos","authors":"Sergey Glyzin, A. Yu. Kolesov","doi":"10.1134/S0016266324040014","DOIUrl":null,"url":null,"abstract":"<p> We propose a mathematical model for a new phenomenon: multi-dimensional hyperbolic chaos. This model is a ring chain of <span>\\(N\\ge 2\\)</span> unidirectionally coupled maps of the two-dimensional torus <span>\\(\\mathbb{T}^2\\)</span>, each of which is of Arnold’s cat map type. We provide sufficient conditions (independent of <span>\\(N\\)</span>) under which the chain gives rise to an Anosov diffeomorphism of <span>\\(\\mathbb{T}^{2N}\\)</span> for any <span>\\(N\\ge 2\\)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"349 - 361"},"PeriodicalIF":0.6000,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Functional Analysis and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S0016266324040014","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a mathematical model for a new phenomenon: multi-dimensional hyperbolic chaos. This model is a ring chain of \(N\ge 2\) unidirectionally coupled maps of the two-dimensional torus \(\mathbb{T}^2\), each of which is of Arnold’s cat map type. We provide sufficient conditions (independent of \(N\)) under which the chain gives rise to an Anosov diffeomorphism of \(\mathbb{T}^{2N}\) for any \(N\ge 2\).
期刊介绍：
Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
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