JournalsjemsVol. 15, No. 6pp. 2043–2060

The entropy conjecture for diffeomorphisms away from tangencies

  • Gang Liao

    Peking University, Beijing, China

  • Marcelo Viana

    IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

  • Jiagang Yang

    Universidade Federal Fluminense - UFF, Niterói, Brazil
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Abstract

We prove that every diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub's entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive.

Cite this article

Gang Liao, Marcelo Viana, Jiagang Yang, The entropy conjecture for diffeomorphisms away from tangencies. J. Eur. Math. Soc. 15 (2013), no. 6, pp. 2043–2060

DOI 10.4171/JEMS/413