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Hyperbolic times: frequency versus integrability

Published online by Cambridge University Press:  09 March 2004

JOSÉ F. ALVES  and
VÍTOR ARAÚJO
JOSÉ F. ALVES
Affiliation:
Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal (e-mail: jfalves@fc.up.pt, vdaraujo@fc.up.pt)
VÍTOR ARAÚJO
Affiliation:
Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal (e-mail: jfalves@fc.up.pt, vdaraujo@fc.up.pt)
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Abstract

We consider dynamical systems on compact manifolds that 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 a (strong) integrability of the first hyperbolic time map implies a positive frequency of hyperbolic times. We also present an example of a map with a 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 2 , April 2004 , pp. 329 - 346
Copyright
2004 Cambridge University Press

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