Recurrence rate in rapidly mixing dynamical systems
Dynamical Systems
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0412211,
title = {Recurrence rate in rapidly mixing dynamical systems},
author = {Benoit Saussol},
journal= {arXiv preprint arXiv:math/0412211},
year = {2007}
}