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Measures of maximal entropy for suspension flows

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Abstract

We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any suspension flow defined over a sub-shift of finite type can be perturbed (by an arbitrarily small perturbation) so that the resulting flow has uncountably many ergodic measures of maximal entropy, and that the same can be arranged so that the new flow has a unique measure of maximal entropy.

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Authors and Affiliations

  1. Facultad de Matemáticas, Pontificia Universidad Católica de Chile (PUC), Avenida Vicuña Mackenna 4860, Santiago, Chile

    Godofredo Iommi

  2. Department of Mathematics, Yale University, New Haven, CT, 06511, USA

    Anibal Velozo

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  1. Godofredo Iommi
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  2. Anibal Velozo
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Correspondence to Anibal Velozo.

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The authors thanks Mike Todd for comments on the article. A.V. would like to thank UC for their hospitality. G.I. was partially supported by Proyecto Fondecyt 1190194 and by CONICYT PIA ACT172001.

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Iommi, G., Velozo, A. Measures of maximal entropy for suspension flows. Math. Z. 297, 1473–1482 (2021). https://doi.org/10.1007/s00209-020-02565-x

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  • DOI: https://doi.org/10.1007/s00209-020-02565-x

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