Dependence with complete connections and the Gauss-Kuzmin theorem for N-continued fractions

Dan Lascu

doi:10.1016/j.jmaa.2016.06.046

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arXiv · 1510.03606

Dependence with complete connections and the Gauss-Kuzmin theorem for N-continued fractions

Dan Lascu

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Abstract

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.

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Dan Lascu. 2015-10-13. Dependence with complete connections and the Gauss-Kuzmin theorem for N-continued fractions. https://doi.org/10.1016/j.jmaa.2016.06.046

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