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Shift endomorphisms and compact Lie extensions

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Abstract

We consider skew-products with an arbitrary compact Lie group, when the base map is a one-sided shift of finite type endowed with an equilibrium state of a Hölder continuous function. First we show that the weak-mixing property of the skew-product implies exactness and exponential mixing. Then we address the problem of classification under measure-theoretic isomorphisms. We show that for a generic set of equilibrium states the isomorphism class of the skew-products corresponds essentially to the cohomology classes of the defining skewing function and the isomorphism is essentially a homeomorphism.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada Faculdade de Ciências, Universidade do Porto, Rua das Taipas, 135, P-4050, Porto, Portugal

    Zaqueu Coelho

  2. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK

    William Parry

Authors
  1. Zaqueu Coelho
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  2. William Parry
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Additional information

Dedicated to Ricardo Mañé

Partially supported by CNPq.

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Coelho, Z., Parry, W. Shift endomorphisms and compact Lie extensions. Bol. Soc. Bras. Mat 29, 163–179 (1998). https://doi.org/10.1007/BF01245872

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  • DOI: https://doi.org/10.1007/BF01245872

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