## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS

We study the time of $n$th return of orbits to some given
(union of) rectangle(s) of a Markov partition for an Axiom A
diffeomorphism. Namely, we prove the existence of a scaled
generating function for these returns with respect to any Gibbs
measure. As a by-product, we derive precise large deviation
estimates and a central limit theorem for these return times. We
emphasize that we look at the limiting behavior in term of number
of visits (the size of the visited set is kept fixed). Our
approach relies on the spectral properties of a one-parameter
family of induced transfer operators on unstable leaves crossing
the visited set.

keywords:
large deviations
,
Successive return times
,
Axiom A
,
central limit theorem.
,
transfer operator

DCDS

We introduce pointwise dimensions and spectra associated with Poincaré
recurrences. These quantities are then calculated for any ergodic measure
of positive entropy on a weakly specified subshift.
We show that they satisfy a relation comparable to Young's formula for the
Hausdorff
dimension of measures invariant under surface diffeomorphisms.
A key-result in establishing these formula is to prove that the Poincaré recurrence for a 'typical' cylinder is asymptotically its length.
Examples are provided which show that this is not true for some systems with
zero entropy.
Similar results are obtained for special flows
and we get a formula relating spectra for measures
of the base to the ones of the flow.

## Year of publication

## Related Authors

## Related Keywords

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