Pressure and recurrence
Volume 178 / 2003
Fundamenta Mathematicae 178 (2003), 129-141
MSC: Primary 37D35.
DOI: 10.4064/fm178-2-3
Abstract
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) $\mathop {\rm lim}_{n\to \infty } n^{-1}\mathop {\rm log}\nolimits \sum _{j=0}^{\tau _n(x)}\mu (\alpha ^n(T^j(x)))$, 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 $\alpha ^n(x)$.
