POINCARÉ RECURRENCE AND TOPOLOGICAL PRESSURE FOR HOMEOMORPHISMS WITH SPECIFICATION

Alejandro M. Mesón (Argentina) and Fernando Vericat (Argentina)

Abstract

We analyze the statistical sum  where t is the time return Poincaré map and      Bn, e  is the ball with centre at x and radius e with respect to the metric dn(x, y) = max {d(f i(x), f i(y)) : i = 0, 1, …, n – 1}.    We obtain the growing rate of the sum in terms of the topological pressure associated to a potential j. The calculation is performed under much weaker hypothesis than a similar one by Maume-Deschamps et al. [Fund. Math. 39 (1993), 78-83].

Keywords and phrases: Poincaré recurrence, specification, expansiveness.