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.
Cite this article
Marcus Bronzi, Ali Tahzibi, Homoclinic tangency and variation of entropy. Port. Math. 77 (2020), no. 3/4, pp. 383–398DOI 10.4171/PM/2055