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Return- and hitting-time limits for rare events of null-recurrent Markov maps

Published online by Cambridge University Press:  13 October 2015

FRANÇOISE PÈNE ,
BENOÎT SAUSSOL  and
ROLAND ZWEIMÜLLER
FRANÇOISE PÈNE
Affiliation:
Laboratoire de Mathématiques de Bretagne Atlantique, CNRS UMR 6205, Université de Bretagne Occidentale, 6, Avenue Victor Le Gorgeu, CS 93837 Brest Cedex 3, France email francoise.pene@univ-brest.fr, benoit.saussol@univ-brest.fr
BENOÎT SAUSSOL
Affiliation:
Laboratoire de Mathématiques de Bretagne Atlantique, CNRS UMR 6205, Université de Bretagne Occidentale, 6, Avenue Victor Le Gorgeu, CS 93837 Brest Cedex 3, France email francoise.pene@univ-brest.fr, benoit.saussol@univ-brest.fr
ROLAND ZWEIMÜLLER
Affiliation:
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria email rzweimue@member.ams.org
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Abstract

We determine limit distributions for return- and hitting-time functions of certain asymptotically rare events for conservative ergodic infinite measure preserving transformations with regularly varying asymptotic type. Our abstract result applies, in particular, to shrinking cylinders around typical points of null-recurrent renewal shifts and infinite measure preserving interval maps with neutral fixed points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 1 , February 2017 , pp. 244 - 276
Copyright
© Cambridge University Press, 2015 

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