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Entry and return times for semi-flows

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)810–824
Number of pages16
JournalNonlinearity
Volume30
Issue number2
Early online date11 Jan 2017
DOIs
DateAccepted/In press - 5 Dec 2016
DateE-pub ahead of print - 11 Jan 2017
DatePublished (current) - 2 Feb 2017

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.

    Research areas

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

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via IOP Publishing at DOI: 10.1088/1361-6544/aa518b. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 218 KB, PDF document

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