{"title":"Invariant Cantor sets in the parametrized Hénon-Devaney map","authors":"B. Leal, Sergio Muñoz","doi":"10.1080/14689367.2021.2012558","DOIUrl":null,"url":null,"abstract":"We consider the (three parameters) family of nonlinear mappings where a, b, c are positive real numbers. is the classical Hénon-Devaney map [1, 2, 6]. For a large open region of parameters, we exhibit invariant Cantor sets embedded in the plane with two hyperbolic fixed points of saddle type.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"105 - 126"},"PeriodicalIF":0.5000,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2021.2012558","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
We consider the (three parameters) family of nonlinear mappings where a, b, c are positive real numbers. is the classical Hénon-Devaney map [1, 2, 6]. For a large open region of parameters, we exhibit invariant Cantor sets embedded in the plane with two hyperbolic fixed points of saddle type.
期刊介绍：
Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal:
•Differential equations
•Bifurcation theory
•Hamiltonian and Lagrangian dynamics
•Hyperbolic dynamics
•Ergodic theory
•Topological and smooth dynamics
•Random dynamical systems
•Applications in technology, engineering and natural and life sciences
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