A Gauss-Kuzmin-type problem for a family of continued fraction expansions

JOURNAL OF NUMBER THEORY

卷:133

Article

Lascu, Dan

关键词: Invariant measure;    Perron-Frobenius operator;    Random system with complete connections;   

DOI  :  10.1016/j.jnt.2012.12.007

来源: Elsevier

【 摘 要 】

In this paper we study in detail a family of continued fraction expansions of any number in the unit closed interval [0,1] whose digits are differences of consecutive non-positive integer powers of an integer m >= 2. For the transformation which generates this expansion and its invariant measure, the Perron-Frobenius operator is given and studied. For this expansion, we apply the method of random systems with complete connections by losifescu and obtained the solution of its Gauss-Kuzmin type problem. (C) 2013 Elsevier Inc. All rights reserved.

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