Pressure and recurrence

Véronique Maume-Deschamps¹ ; Bernard Schmitt² ; Mariusz Urbański³ ; Anna Zdunik⁴

¹ Laboratoire de Topologie B.P. 47 870 21078 Dijon Cedex, France
² Laboratoire de Topologie B.P. 47 870 21078-Dijon Cedex, France
³ Department of Mathematics University of North Texas Denton, TX 76203-1430, U.S.A.
⁴ Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland

Fundamenta Mathematicae, Tome 178 (2003) no. 2, pp. 129-141.

Résumé

We deal with a subshift of finite type and an equilibrium state $\mu$ for a Hölder continuous function. Let ${\alpha }^n$ be the partition into cylinders of length $n$. We compute (in particular we show the existence of the limit) ${\lim }_{n\to \mathrm{\infty }}{n}^{-1}\log \sum _{j=0}^{{\tau }_n(x)}\mu ({\alpha }^n(T^j(x)))$, where ${\alpha }^n(T^j(x))$ is the element of the partition containing $T^j(x)$ and ${\tau }_n(x)$ is the return time of the trajectory of $x$ to the cylinder ${\alpha }^n(x)$.

Détail

DOI : 10.4064/fm178-2-3

Mots-clés : subshift finite type equilibrium state lder continuous function alpha partition cylinders length compute particular existence limit mathop lim infty mathop log nolimits sum tau alpha x where alpha element partition containing tau return time trajectory cylinder alpha