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Journal of Function Spaces
Volume 2014 (2014), Article ID 980461, 12 pages
Research Article

A Gauss-Kuzmin Theorem and Related Questions for θ-Expansions

1Faculty of Applied Sciences, Politehnica University of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania
2Mircea cel Batran Naval Academy, 1 Fulgerului, 900218 Constanta, Romania

Received 23 May 2013; Accepted 3 December 2013; Published 11 February 2014

Academic Editor: Messaoud Bounkhel

Copyright © 2014 Gabriela Ileana Sebe and Dan Lascu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Using the natural extension for θ-expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotients of these expansions. Together with the ergodic behavior of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the previous fraction expansion.