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Dependence with complete connections and the Gauss-Kuzmin theorem for \(N\)-continued fractions. (English) Zbl 1358.37074

J. Math. Anal. Appl. 444, No. 1, 610-623 (2016); corrigendum ibid. 447, No. 1, 681 (2017).
Summary: We consider a family \(\{T_N : N \geq 1 \}\) of interval maps as generalizations of the Gauss transformation. For the continued fraction expansion arising from \(T_N\), we solve its Gauss-Kuzmin-type problem by applying the theory of random systems with complete connections by Iosifescu.

MSC:

37E05 Dynamical systems involving maps of the interval
11A55 Continued fractions
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