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On $C^0$-centralizers of Anosov diffeomorphisms on the torus: algebraic and topological aspects

Volume 258 / 2022

Jorge Rocha, Paulo Varandas Fundamenta Mathematicae 258 (2022), 1-24 MSC: Primary 37D20, 37C20, 37C15; Secondary 37F15, 37C05. DOI: 10.4064/fm969-10-2020 Published online: 25 April 2022


Anosov diffeomorphisms on $\mathbb T^d$ are well known to be topologically conjugate to hyperbolic automorphisms induced by integer valued matrices. We show that in general the internal algebraic structures of the centralizers of such hyperbolic matrices, in the multiplicative group of all integer matrices with determinant $\pm 1$, are not sufficient to determine the matrix centralizers of the automorphisms and, ultimately, the $C^0$-centralizers of the original Anosov diffeomorphisms. We also obtain necessary and sufficient conditions, relying on entropy sequences, for the centralizer to be elementary.


  • Jorge RochaDepartamento de Matemática
    Universidade do Porto
    Rua do Campo Alegre, 687
    4169-007 Porto, Portugal
  • Paulo VarandasDepartamento de Matemática e Estatística
    Universidade Federal da Bahia
    Av. Ademar de Barros s/n
    40170-110 Salvador, Brazil

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