Anosov endomorphisms on the two-torus: regularity of foliations and rigidity
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Published:2023-09-01
Issue:10
Volume:36
Page:5334-5357
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ISSN:0951-7715
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Container-title:Nonlinearity
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language:
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Short-container-title:Nonlinearity
Author:
Cantarino MarisaORCID,
Varão Régis
Abstract
Abstract
We provide sufficient conditions for smooth conjugacy between two Anosov endomorphisms on the two-torus. From that, we also explore how the regularity of the stable and unstable foliations implies smooth conjugacy inside a class of endomorphisms including, for instance, the ones with constant Jacobian. As a consequence, we have in this class a characterisation of smooth conjugacy between special Anosov endomorphisms (defined as those having only one unstable direction for each point) and their linearisations.
Funder
Fundação de Amparo à Pesquisa do Estado de São Paulo
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
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