Abstract
It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension of exceptional sets arising from dynamics.
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Acknowledgments
The author acknowledges the partial supported by EPSRC. He is grateful to Manfred Einsiedler for referring to [15]. He also would like to thank René Rühr and anonymous referee for useful comments for the preliminary version of the article.
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Communicated by H. Bruin.
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Kadyrov, S. Effective uniqueness of Parry measure and exceptional sets in ergodic theory. Monatsh Math 178, 237–249 (2015). https://doi.org/10.1007/s00605-014-0690-7
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DOI: https://doi.org/10.1007/s00605-014-0690-7