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Sufficient condition for the hyperbolicity of mappings of the torus

Sufficient condition for the hyperbolicity of mappings of the torus We consider mappings of the m-dimensional torus Tm (m ≥ 2) that are C 1-perturbations of linear hyperbolic automorphisms. We obtain sufficient conditions for such mappings to be one-to-one hyperbolic mappings (i.e., Anosov diffeomorphisms). These results are used to study the blue-sky catastrophe related to the vanishing of a saddle-node invariant torus with a quasiperiodic winding in a system of ordinary differential equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Sufficient condition for the hyperbolicity of mappings of the torus

Differential Equations , Volume 53 (4) – May 17, 2017

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References (13)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S001226611704005X
Publisher site
See Article on Publisher Site

Abstract

We consider mappings of the m-dimensional torus Tm (m ≥ 2) that are C 1-perturbations of linear hyperbolic automorphisms. We obtain sufficient conditions for such mappings to be one-to-one hyperbolic mappings (i.e., Anosov diffeomorphisms). These results are used to study the blue-sky catastrophe related to the vanishing of a saddle-node invariant torus with a quasiperiodic winding in a system of ordinary differential equations.

Journal

Differential EquationsSpringer Journals

Published: May 17, 2017

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