A dependence with complete connections approach to generalized R\'enyi continued fractions
Number Theory
2018-10-25 v1
Abstract
We introduce and study in detail a special class of backward continued fractions that represents a generalization of R\'enyi continued fractions. We investigate the main metrical properties of the digits occurring in these expansions and we construct the natural extension for the transformation that generates the R\'enyi-type expansion. Also we define the associated random system with complete connections whose ergodic behavior allows us to prove a variant of Gauss-Kuzmin-type theorem.
Keywords
Cite
@article{arxiv.1810.10246,
title = {A dependence with complete connections approach to generalized R\'enyi continued fractions},
author = {Gabriela Ileana Sebe and Dan Lascu},
journal= {arXiv preprint arXiv:1810.10246},
year = {2018}
}
Comments
18 pages