On non-trivial hyperbolic sets and their bifurcations in families of diffeomorphisms of a two-dimensional torus

被引：0

作者：

Kazakov, Alexey ^{[1
]}

Mints, Dmitrii ^{[2
]}

Petrova, Iuliia ^{[1
]}

Shilov, Oleg ^{[1
]}

机构：

[1] Natl Res Univ Higher Sch Econ, Lab Dynam Syst & Applicat, 25-12 Bolshaya Pecherskaya Ulitsa, Nizhnii Novgorod 603155, Russia

[2] Imperial Coll London, Dept Math, London SW7 2AZ, England

来源：

CHAOS | 2024年 / 34卷 / 08期

基金：

英国工程与自然科学研究理事会;

关键词：

CLASSIFICATION; ATTRACTORS; SYSTEMS;

D O I：

10.1063/5.0211890

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a simple model-two-parameter family of diffeomorphisms of a two-dimensional torus. Combining analytical and numerical methods, we find regions in the parameter plane such that each diffeomorphism of the family is hyperbolic and describe the structure of the corresponding hyperbolic sets. We also study bifurcations on the boundaries of these regions, which lead to the change of hyperbolicity type (from Anosov diffeomorphisms to DA-diffeomorphisms).

引用

页数：11

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