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2008, Volume 21, Issue 4: 1103-1128. Doi: 10.3934/dcds.2008.21.1103
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Generic points in systems of specification and Banach valued Birkhoff ergodic average

  • 1.

    Department of Mathematics, Wuhan University, 430072 Wuhan

  • 2.

    CNRS UMR 6140, Université de Picardie Jules Verne, 33, Rue Saint Leu, 80039 Amiens Cedex 1

  • 3.

    Université Paris-Sud, CNRS UMR 8628, Mathématique bât. 425, 91405 Orsay Cedex

Received:  April 30, 2007
Revised:  March 31, 2008
Published:  September 2008
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 37B40, 37B45; Secondary: 37A05.

    Citation:
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