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Return-Time Statistics, Hitting-Time Statistics and Inducing

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Ergodic Theory, Open Dynamics, and Coherent Structures

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 70))

Abstract

In the framework of abstract ergodic probability-preserving transformations, we prove that the limiting return-time statistics and hitting-time statistics persist if we pass from the original system to a first-return map and vice versa.

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Notes

  1. 1.

    This is obviously a property of the sequence and not of the individual events H l . Still, we take the liberty of following this imprecise but common terminology.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

    Nicolai T. A. Haydn

  2. FB Mathematik, Universität Salzburg, Hellbrunner Strasse 34, 5020, Salzburg, Austria

    Nicole Winterberg

  3. Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Roland Zweimüller

Authors
  1. Nicolai T. A. Haydn
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  2. Nicole Winterberg
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  3. Roland Zweimüller
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Corresponding author

Correspondence to Nicolai T. A. Haydn .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University, Leicestershire, Leicestershire, United Kingdom

    Wael Bahsoun

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    Christopher Bose

  3. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Gary Froyland

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Haydn, N.T.A., Winterberg, N., Zweimüller, R. (2014). Return-Time Statistics, Hitting-Time Statistics and Inducing. In: Bahsoun, W., Bose, C., Froyland, G. (eds) Ergodic Theory, Open Dynamics, and Coherent Structures. Springer Proceedings in Mathematics & Statistics, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0419-8_10

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