Maximal Entropy Measures for Piecewise Affine Surface Homeomorphisms

Jerome Buzzi (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability measures maximizing entropy and prove a multiplicative lower bound for the number of periodic points. This is intended as a step towards the understanding of surface diffeomorphisms. We proceed by building a jump transformation, using not first returns but carefully selected ``good'' returns to dispense with Markov partitions. We control these good returns through some entropy and ergodic arguments.

Mots clés: Dynamical systems; ergodic theory; topological entropy; variational principle; measures with maximum entropy; Markov structure; Markov tower; symbolic dynamics; coding

Domaines: Systèmes dynamiques [math.DS]

Jerome Buzzi. Maximal Entropy Measures for Piecewise Affine Surface Homeomorphisms. 2007. ⟨hal-00171744v2⟩