Generic points in systems of specification and Banach valued Birkhoff ergodic average
Dynamical Systems
2008-02-26 v1
Abstract
We prove that systems satisfying the specification property are saturated in the sense that the topological entropy of the set of generic points of any invariant measure is equal to the measure-theoretic entropy of the measure. We study Banach valued Birkhoff ergodic averages and obtain a variational principle for its topological entropy spectrum. As application, we examine a particular example concerning with the set of real numbers for which the frequencies of occurrences in their dyadic expansions of infinitely many words are prescribed. This relies on our explicit determination of a maximal entropy measure.
Cite
@article{arxiv.0802.3434,
title = {Generic points in systems of specification and Banach valued Birkhoff ergodic average},
author = {Ai-Hua Fan and Lingmin Liao and Jacques Peyrière},
journal= {arXiv preprint arXiv:0802.3434},
year = {2008}
}
Comments
accepted by Discrete and Continuous Dynamical Systems