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k-limit laws of return and hitting times

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


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