A+ CATEGORY SCIENTIFIC UNIT

Pressure and recurrence

Volume 178 / 2003

Véronique Maume-Deschamps, Bernard Schmitt, Mariusz Urbański, Anna Zdunik 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 $\alpha ^n(x)$.

Authors

  • Véronique Maume-DeschampsLaboratoire de Topologie
    B.P. 47 870
    21078 Dijon Cedex, France
    e-mail
  • Bernard SchmittLaboratoire de Topologie
    B.P. 47 870
    21078-Dijon Cedex, France
    e-mail
  • Mariusz UrbańskiDepartment of Mathematics
    University of North Texas
    Denton, TX 76203-1430, U.S.A.
    e-mail
  • Anna ZdunikInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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