Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients
نویسنده
چکیده
We prove the existence of the limiting distribution for the sequence of denominators generated by continued fraction expansions with even partial quotients, which were introduced by F. Schweiger [14] [15] and studied also by C. Kraaikamp and A. Lopes [10]. Our main result is proven following the strategy used by Ya. Sinai and C. Ulcigrai [18] in their proof of a similar renewal-type theorem for Euclidean continued fraction expansions and the Gauss map. The main steps in our proof are the construction of a natural extension of a Gauss-like map and the proof of mixing of a related special flow.
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تاریخ انتشار 2008