Symbolic extensions in intermediate smoothness on surfaces

David Burguet (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

We prove that $\mathcal{C}^r$ maps with $r>1$ on a compact surface have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. More precisely we give a sharp upper bound on the so-called symbolic extension entropy, which is the infimum of the topological entropies of all the symbolic extensions. This answers positively a conjecture of S.Newhouse and T.Downarowicz in dimension two and improves a previous result of the author \cite{burinv}.

Mots clés: Systèmes dynamiques différentiables; Théorie ergodique; Entropie; Extensions symboliques.; Extensions symboliques

Domaines: Systèmes dynamiques [math.DS]

David Burguet. Symbolic extensions in intermediate smoothness on surfaces. 2011. ⟨hal-00578001v2⟩