Pressure and recurrence
Fundamenta Mathematicae, Tome 178 (2003) no. 2, p. 129.

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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 → ∞ n - 1 l o g ∑ 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).
Classification : 37B10, 37B35, 37A05, 37D35
Mots-clés : thermodynamic formalism, variational principle, equilibrium states, measure-preserving transformtion, subshift of finite type 
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Véronique Maume-Deschamps; Bernard Schmitt; Mariusz Urbański; Anna Zdunik. Pressure and recurrence. Fundamenta Mathematicae, Tome 178 (2003) no. 2, p. 129. https://geodesic-test.mathdoc.fr/item/FUNDAM_2003__178_2_282851/