k-limit laws of return and hitting times

V. Chaumoître; M. Kupsa

doi:10.3934/dcds.2006.15.73

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2006, Volume 15, Issue 1: 73-86. Doi: 10.3934/dcds.2006.15.73

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k-limit laws of return and hitting times

V. Chaumoître^1, and
M. Kupsa^2,

1.
LAMFA, Université de Picardie Jules Verne, 33, rue Saint Leu 80000 Amiens
2.
Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou vêží 4, Praha 8

Received: January 2005

Revised: October 2005

Published: March 2006

Abstract / Introduction Related Papers Cited by

Abstract

We characterize the set Ḟ of possible $k$-limit laws of return times which appears to be independent of $k$. We construct a rank-one system having all the functions of Ḟ as a $k$-limit law of return times. We exhibit a link between $k$-limit laws of return and hitting times. We conclude with a discussion over the $n$-uples ($1$-limit law, ..., $n$-limit law) of return times.

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Mathematics Subject Classification: 37A05, 60F05, 28D05.

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