Symbolic extensions for nonuniformly entropy expanding maps

• Autorzy: David Burguet
• Języki publikacji: EN

Abstrakty

EN

A nonuniformly entropy expanding map is any 𝓒¹ map defined 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 [Invent. Math. 176 (2009)].

Kategorie tematyczne

• 37C40: Smooth ergodic theory, invariant measures
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 121
• Numer: 1
• Strony: 129-151

Daty

wydano

2010

Twórcy

autor

David Burguet

• CMLA-ENS Cachan, 61 avenue du président Wilson, 94235 Cachan Cedex, France

Identyfikatory

DOI

10.4064/cm121-1-12