Abstract: We
analyze the statistical sum where t
is the time return Poincaré map and Bn,
eis
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.
