Generic points of shift-invariant measures in the countable symbolic space - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematical Proceedings of the Cambridge Philosophical Society Année : 2019

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

(1) , ,
1
Ming-Tian Li
  • Fonction : Auteur
Ji-Hua Ma
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-03622000 , version 1 (28-03-2022)

Identifiants

Citer

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, 2019, 166 (2), pp.381-413. ⟨10.1017/S0305004118000038⟩. ⟨hal-03622000⟩
6 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook Twitter LinkedIn More