Entropy pairs and a local Abramov formula for a measure theoretical entropy of open covers

HUANG W.; Maass A.; Romagnoli, PP; Ye X.

Abstract

Let (X, T) be a topological dynamical system and let ? be a T-invariant probability measure on X. In this paper, we study two properties of the notions of measure theoretical entropy for a measurable cover U, h?+(U, T) and h?-(U, T) introduced by P. P. Romagnoli (Ergod. Th. & Dynam. Sys. 23 (2003), 1601-1610). The main result of the paper states that entropy pairs for the measure ? can be defined using either h?+ or h?-. We also prove that both h?+ and h?- have an ergodic decomposition and we use it to prove a local Abramov formula for h?-.

Más información

Título según WOS: Entropy pairs and a local Abramov formula for a measure theoretical entropy of open covers
Título según SCOPUS: Entropy pairs and a local Abramov formula for a measure theoretical entropy of open covers
Título de la Revista: ERGODIC THEORY AND DYNAMICAL SYSTEMS
Volumen: 24
Número: 4
Editorial: CAMBRIDGE UNIV PRESS
Fecha de publicación: 2004
Página de inicio: 1127
Página final: 1153
Idioma: English
URL: http://www.journals.cambridge.org/abstract_S0143385704000161
DOI:

10.1017/s0143385704000161

Notas: ISI, SCOPUS