Hitting and escaping statistics: mixing, targets and holes
Dynamical Systems
2018-01-08 v2
Abstract
There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one can move through a natural parameter space from one to the other. On the other hand, if the mixing is subexponential, there is a phase transition between the hitting times law and the escape law.
Keywords
Cite
@article{arxiv.1609.01196,
title = {Hitting and escaping statistics: mixing, targets and holes},
author = {Henk Bruin and Mark F. Demers and Mike Todd},
journal= {arXiv preprint arXiv:1609.01196},
year = {2018}
}
Comments
31 pages. To appear in Advances in Mathematics