Entry and return times for semi-flows
Dynamical Systems
2017-02-01 v2 Probability
Abstract
Haydn, Lacroix and Vaienti [Ann. Probab. 33 (2005)] proved that, for a given ergodic map, the entry time distribution converges in the small target limit, if and only if the corresponding return time distribution converges. The present note explains how entry and return times can be interpreted in terms of stationary point processes and their Palm distribution. This permits a generalization of the results by Haydn et al. to non-ergodic maps and continuous-time dynamical systems.
Cite
@article{arxiv.1605.02715,
title = {Entry and return times for semi-flows},
author = {Jens Marklof},
journal= {arXiv preprint arXiv:1605.02715},
year = {2017}
}
Comments
14 pages; to appear in Nonlinearity