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Homoclinic tangency and variation of entropy

Bronzi, Marcus ; Tahzibi, Ali

Portugaliae mathematica, 2020-01, Vol.77 (3), p.383-398 [Periódico revisado por pares]

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Título:
Homoclinic tangency and variation of entropy
Autor: Bronzi, Marcus ; Tahzibi, Ali
Assuntos: Algebraic topology ; Dynamical systems ; Dynamical systems and ergodic theory ; Isomorphisms (Mathematics) ; Mathematical research ; Topology
É parte de: Portugaliae mathematica, 2020-01, Vol.77 (3), p.383-398
Descrição: 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 $C^{\infty}$-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.
Editor: Zuerich, Switzerland: European Mathematical Society Publishing House
Idioma: Inglês

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