Generic points in systems of specification and Banach valued Birkhoff ergodic average

By A. Fan, Lingmin Liao, J. Peyriére. 2008

54 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1c97559ed1a6b715fedbd4abe2c26b977b7bd7b8

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In Mathematical Physics

1. Wen Huang
2. De-Jun Feng
3. Xiangdong Ye
4. A. Kaenmaki
5. Eli Glasner
6. Huyi Hu
7. Jian Li
8. Guohua Zhang

Citations in the corpus

• Lyapunov Spectrum of Asymptotically Sub-additive Potentials (2009, background): “It was shown independently in [22, 44] that if a TDS (X,T ) satisfies the specification property, then (X,T ) is saturated.”