# American Institute of Mathematical Sciences

2006, 15(1): 73-86. doi: 10.3934/dcds.2006.15.73

## k-limit laws of return and hitting times

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

Received  January 2005 Revised  October 2005 Published  February 2006

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.
Citation: V. Chaumoître, M. Kupsa. k-limit laws of return and hitting times. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 73-86. doi: 10.3934/dcds.2006.15.73
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