Sufficient condition for the hyperbolicity of mappings of the torus |
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Authors: | A Yu Kolesov N Kh Rozov V A Sadovnichii |
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Institution: | 1.Demidov Yaroslavl State University,Yaroslavl,Russia;2.Lomonosov Moscow State University,Moscow,Russia |
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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. |
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