## 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
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

For Axiom A diffeomorphisms and equilibrium states, we prove a Large deviations result for the sequence of successive return times into a fixed Borel set, under some assumption on the boundary.
Our result relies on and extends the work by Chazottes and Leplaideur who considered cylinder sets of a Markov partition.

DCDS

For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point.
We prove that when the decay of correlation is super-polynomial the recurrence rates and the pointwise dimensions are equal.
This gives a broad class of systems for which the recurrence rate equals the Hausdorff dimension of the invariant measure.

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.

JCD

We show an elementary method to obtain (finite time and asymptotic) computer assisted explicit upper bounds on convergence to equilibrium (decay of correlations) and escape rates for systems satisfying a Lasota Yorke inequality. The bounds are deduced from the ones of suitable approximations of the system's transfer operator. We also present some rigorous experiments on some nontrivial example.

DCDS

In this paper we give new properties of the dimension introduced
by Afraimovich to characterize Poincaré recurrence and which we proposed to
call Afraimovich-Pesin's (AP's) dimension. We will show in particular that
AP's dimension is a topological invariant and that it often coincides with the
asymptotic distribution of periodic points : deviations from this behavior could
suggest that the AP's dimension is sensitive to some
"non-typical" points.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]