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

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).

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Publication Details

Journal
Chaos An Interdisciplinary Journal of Nonlinear Science
Published
2024-08-01
DOI
https://doi.org/10.1063/5.0211890
Primary Topic
Mathematical Dynamics and Fractals
Type
article
Field-Weighted Citation Impact
0.00

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article

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

I. V. Petrova, Dmitrii Mints, Alexey Kazakov, Oleg Shilov
Chaos An Interdisciplinary Journal of Nonlinear Science
Mathematical Dynamics and Fractals
article

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

I. V. Petrova, Dmitrii Mints, Alexey Kazakov, Oleg Shilov
article en

Abstract

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).

Chaos An Interdisciplinary Journal of Nonlinear ScienceVol. 34(8)
National Research University Higher School of Economics (RU), Imperial College London (GB)
Leverhulme Trust, Russian Science Foundation, National Research University Higher School of Economics, EPSRC Centre for Doctoral Training in Additive Manufacturing
Openalex Percentile: Top 77%
Mathematical Dynamics and Fractals
DOISourceOpenAlex
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On non-trivial hyperbolic sets and their bifurcations in families of diffeomorphisms of a two-dimensional torus — I. V. Petrova, Dmitrii Mints, et al. · Chaos An Interdisciplinary Journal of Nonlinear Science (2024) | TGRS Research Map | TGRS