Entry and return times for semi-flows

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.

14 pages; to appear in Nonlinearity

References in corpus (4)

• Extremes and Recurrence in Dynamical Systems
• Rare Events for the Manneville-Pomeau map
• Hitting time statistics for observations of dynamical systems
• Santalo's formula and stability of trapping sets of positive measure

Cited by in corpus (4)

• Extreme events for horocycle flows
• On convergence of points to limiting processes, with an application to zeta zeros
• Fine-scale distribution of roots of quadratic congruences
• Hitting times distribution and extreme value law for flows