2008/02/29 by Francesco Cellarosi, Cellarosi, Francesco
Economics, Econometrics and Finance · Mathematics · #11J70 #11K50 (Primary) #28D05 #37E05 #60F99 #60K05 (Secondary) #Analytic Number Theory Research #Discrete mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Geology #Limit (mathematics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematical economics #Mathematics #Pure mathematics #Quotient #Stochastic processes and financial applications #Type (biology) #math.DS #msc:11J70 #msc:11K50 #msc:28D05 #msc:37E05 #msc:60F99 #msc:60K05
paper · pdf · doi:10.48550/arxiv.0802.4459
published in arXiv (Cornell University) (Cornell University) · 27 pages, 3 figures, some typos corrected, section 2 expanded, final version to appear in "Ergodic Theory and Dynamical Systems"
openalex publication_date 2008/02/29 · arxiv created 2008/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.