The R'enyi Entropy Function and the Large Deviation of Short Return Times

Nicolai Haydn (1) , Sandro Vaienti (2, 3)

1 USC - University of Southern California
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

We consider the R'enyi entropy function for weakly -mixing systems. The first main result proves existence and regularity properties. The second main result of the paper is to get the decay rate for the large deviation of the return time to cylinder sets. We show it to be exponential with a rate given by the R'enyi entropy function. Finally we also obtain bounds for the free energy.

Domaines: Systèmes dynamiques [math.DS]

Nicolai Haydn, Sandro Vaienti. The R'enyi Entropy Function and the Large Deviation of Short Return Times. Ergodic Theory and Dynamical Systems, 2010, 30, pp.159-179. ⟨10.1017/S0143385709000030⟩. ⟨hal-00294306⟩