Pressure and recurrence

Véronique Maume-Deschamps; Bernard Schmitt; Mariusz Urbański; Anna Zdunik

Véronique Maume-Deschamps ; Bernard Schmitt ; Mariusz Urbański ; Anna Zdunik

Fundamenta Mathematicae, Tome 177 (2003), p. 129-141 / Harvested from The Polish Digital Mathematics Library

Résumé

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) $l i m_{n \to \infty} n^{- 1} l o g \sum_{j = 0}^{τ ₙ (x)} μ (α ⁿ (T^{j} (x)))$ , where $α ⁿ (T^{j} (x))$ 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).

Publié le : 2003-01-01

Zbl 1047.37006

EUDML-ID : urn:eudml:doc:282851

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     title = {Pressure and recurrence},
     journal = {Fundamenta Mathematicae},
     volume = {177},
     year = {2003},
     pages = {129-141},
     zbl = {1047.37006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-2-3}
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Véronique Maume-Deschamps; Bernard Schmitt; Mariusz Urbański; Anna Zdunik. Pressure and recurrence. Fundamenta Mathematicae, Tome 177 (2003) pp. 129-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-2-3/