Hyperbolic times: frequency vs. integrability

Details Hyperbolic times: frequency vs. integrability Hyperbolic times: frequency vs. integrability

2003-11-25

arxiv.org/abs/math/0311440v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

We consider dynamical systems on compact manifolds, which are local diffeomorphisms outside an exceptional set (a compact submanifold). We are interested in analyzing the relation between the integrability (with respect to Lebesgue measure) of the first hyperbolic time map and the existence of positive frequency of hyperbolic times. We show that some (strong) integrability of the first hyperbolic time map implies positive frequency of hyperbolic times. We also present an example of a map with positive frequency of hyperbolic times at Lebesgue almost every point but whose first hyperbolic time map is not integrable with respect to the Lebesgue measure.

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