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math.DS2007
Renewal-type Limit Theorem for the Gauss Map and Continued Fractions
Yakov G. Sinai, Corinna Ulcigrai
In this paper we prove the following renewal-type limit theorem. Given an irrational in (0,1) and R>0, let be the first denominator of the convergents of which ex…
math.DS2007
A Limit Theorem for Birkoff sums of non-integrable functions over rotations
Yakov G. Sinai, Corinna Ulcigrai
We consider Birkhoff sums of functions with a singularity of type 1/x over rotations and prove the following limit theorem. Let be the N^th non-renormalized Birkhof…