Entry and return times for semi-flows

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Abstract

Haydn, Lacroix and Vaienti (2005 Ann. Probab. 33 2043–50) 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.
Original languageEnglish
Pages (from-to)810–824
Number of pages16
JournalNonlinearity
Volume30
Issue number2
Early online date11 Jan 2017
DOIs
Publication statusPublished - 2 Feb 2017

Keywords

  • return times
  • Kac formula
  • palm distribution
  • point process Mathematics Subject Classification numbers: 37A10, 60G55

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