Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients

Details Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients

2008-02-29

arxiv.org/abs/0802.4459v2

Mathematics

Dynamical Systems

27 pages, 3 figures, some typos corrected, section 2 expanded, final version to appear in "Ergodic Theory and Dynamical System

Scientific paper

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 and studied also by C. Kraaikamp and A. Lopes. Our main result is proven following the strategy used by Ya. Sinai and C. Ulcigrai 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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