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Generic points of shift-invariant measures in the countable symbolic space

Abstract : We are concerned with sets of generic points for shift-invariant measures in the countable symbolic space. We measure the sizes of the sets by the Billingsley-Hausdorff dimensions defined by Gibbs measures. It is shown that the dimension of such a set is given by a variational principle involving the convergence exponent of the Gibbs measure and the relative entropy dimension of the Gibbs measure with respect to the invariant measure. This variational principle is different from that of the case of finite symbols, where the convergent exponent is zero and is not involved. An application is given to a class of expanding interval dynamical systems.
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https://hal-u-picardie.archives-ouvertes.fr/hal-03622000
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Soumis le : lundi 28 mars 2022 - 16:23:19
Dernière modification le : mercredi 14 septembre 2022 - 18:00:24

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Ai-Hua Fan, Ming-Tian Li, Ji-Hua Ma. Generic points of shift-invariant measures in the countable symbolic space. Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press (CUP), 2019, 166 (2), pp.381-413. ⟨10.1017/S0305004118000038⟩. ⟨hal-03622000⟩

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