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On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves

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Abstract

In this paper we study the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms defined on 3-torus with compact center leaves. Assuming the existence of a periodic leaf with Morse–Smale dynamics we prove a sharp upper bound for the number of maximal measures in terms of the number of sources and sinks of Morse–Smale dynamics. A well-known class of examples for which our results apply are the so called Kan-type diffeomorphisms admitting physical measures with intermingled basins.

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Notes

  1. This is sometimes called pointwise domination, see [1].

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo (USP), São Carlos, Brazil

    Ali Tahzibi

  2. Unidade Acadêmica de Cabo de Santo Agostinho, Universidade Federal Rural de Pernambuco, Recife, Brazil

    Joas Elias Rocha

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  1. Joas Elias Rocha
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  2. Ali Tahzibi
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Ali Tahzibi is supported by FAPESP 107/06463-3 and CNPq (PQ) 303025/2015-8.

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Rocha, J.E., Tahzibi, A. On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves. Math. Z. 301, 471–484 (2022). https://doi.org/10.1007/s00209-021-02925-1

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