Dependence with complete connections and the Gauss-Kuzmin theorem for N-continued fractions
Abstract
We consider a family \TN:N ≥ 1 \ of interval maps as generalizations of the Gauss transformation. For the continued fraction expansion arising from TN, we solve its Gauss-Kuzmin-type problem by applying the theory of random systems with complete connections by Iosifescu.
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