Homoclinic tangency and variation of entropy

  • Marcus Bronzi

    Universidade Federal de Uberlândia, Brazil
  • Ali Tahzibi

    Universidade de São Paulo, São Carlos, Brazil
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In this paper we study the e¤ect of a homoclinic tangency in the variation of the topological entropy. We prove that a diffeomorphism with a homoclinic tangency associated to a basic hyperbolic set with maximal entropy is a point of entropy variation in the -topology. We also prove results about variation of entropy in other topologies and when the tangency does not correspond to a basic set with maximal entropy. We also show an example of discontinuity of the entropy among diffeomorphisms of three dimensional manifolds.

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Marcus Bronzi, Ali Tahzibi, Homoclinic tangency and variation of entropy. Port. Math. 77 (2020), no. 3/4, pp. 383–398

DOI 10.4171/PM/2055