On a Gauss-Kuzmin-Type Problem for a Family of Continued Fraction Expansions
Abstract
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 Iosifescu and obtained the solution of its Gauss-Kuzmin type problem.
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