International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 20, Pages 1067-1076

A Gauss-Kuzmin-Lévy theorem for a certain continued fraction

Hei-Chi Chan

Mathematical Sciences Program, University of Illinois, Springfield 62794-9243, IL, USA

Received 2 April 2003

Copyright © 2004 Hei-Chi Chan. 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.


We consider an interval map which is a generalization of the well-known Gauss transformation. In particular, we prove a result concerning the asymptotic behavior of the distribution functions of this map.