Pressure and recurrence

Véronique Maume-Deschamps, et al. "Pressure and recurrence." Fundamenta Mathematicae 178.2 (2003): 129-141. <http://eudml.org/doc/282851>.

@article{VéroniqueMaume2003,
abstract = {We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) $lim_\{n→∞\} n^\{-1\} log ∑_\{j=0\}^\{τₙ(x)\} μ(αⁿ(T^j(x)))$, where $αⁿ(T^j(x))$ is the element of the partition containing $T^j(x)$ and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).},
author = {Véronique Maume-Deschamps, Bernard Schmitt, Mariusz Urbański, Anna Zdunik},
journal = {Fundamenta Mathematicae},
keywords = {thermodynamic formalism; variational principle; equilibrium states; measure-preserving transformtion; subshift of finite type},
language = {eng},
number = {2},
pages = {129-141},
title = {Pressure and recurrence},
url = {http://eudml.org/doc/282851},
volume = {178},
year = {2003},
}

TY - JOUR
AU - Véronique Maume-Deschamps
AU - Bernard Schmitt
AU - Mariusz Urbański
AU - Anna Zdunik
TI - Pressure and recurrence
JO - Fundamenta Mathematicae
PY - 2003
VL - 178
IS - 2
SP - 129
EP - 141
AB - We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) $lim_{n→∞} n^{-1} log ∑_{j=0}^{τₙ(x)} μ(αⁿ(T^j(x)))$, where $αⁿ(T^j(x))$ is the element of the partition containing $T^j(x)$ and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).
LA - eng
KW - thermodynamic formalism; variational principle; equilibrium states; measure-preserving transformtion; subshift of finite type
UR - http://eudml.org/doc/282851
ER -