SYMBOLIC EXTENSIONS FOR NONUNIFORMLY ENTROPY EXPANDING MAPS

David Burguet (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

We call nonuniformly entropy expanding map any C^1 map dened on a compact manifold whose ergodic measures with positive entropy have only nonnegative Lyapunov exponents. We prove that a C^r nonuniformly entropy expanding map T with r > 1 has a symbolic extension and we give an explicit upper bound of the symbolic extension entropy in terms of the positive Lyapunov exponents by following the approach of T.Downarowicz and A.Maass[14].

Domaines: Systèmes dynamiques [math.DS]

David Burguet. SYMBOLIC EXTENSIONS FOR NONUNIFORMLY ENTROPY EXPANDING MAPS. 2010. ⟨hal-00464826⟩