Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients
Dynamical Systems
2008-08-05 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0802.4459,
title = {Renewal-type Limit Theorem for Continued Fractions with Even Partial Quotients},
author = {Francesco Cellarosi},
journal= {arXiv preprint arXiv:0802.4459},
year = {2008}
}
Comments
27 pages, 3 figures, some typos corrected, section 2 expanded, final version to appear in "Ergodic Theory and Dynamical Systems"