{"title":"Building Expansion for Generalizations of Viana Maps","authors":"Vanderlei Horita, Nivaldo Muniz, Olivier Sester","doi":"10.1007/s10884-024-10357-8","DOIUrl":null,"url":null,"abstract":"<p>We study a family of skew-products of smooth functions having a unique critical point of degree <span>\\(D\\ge 2\\)</span> over a strongly expanding map of the circle and prove that these systems admit two positive Lyapunov exponents. This extends an analogous result of Viana who considered, in the seminal paper (Viana in Inst Hautes Études Sci Publ Math 85:63–96, 1997), the quadratic case <span>\\(D=2\\)</span>.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"86 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10884-024-10357-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study a family of skew-products of smooth functions having a unique critical point of degree \(D\ge 2\) over a strongly expanding map of the circle and prove that these systems admit two positive Lyapunov exponents. This extends an analogous result of Viana who considered, in the seminal paper (Viana in Inst Hautes Études Sci Publ Math 85:63–96, 1997), the quadratic case \(D=2\).
期刊介绍：
Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.
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