Homoclinic tangency and variation of entropy

In this paper we study the effect 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 $C^{\infty}$-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 $C^{\infty}$ diffeomorphisms of three dimensional manifolds.

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