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arXiv · 1707.08393

A two-dimensional Gauss-Kuzmin theorem for $N$-continued fraction expansions

Gabriela Ileana Sebe·Dan Lascu
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Abstract

A two-dimensional Gauss-Kuzmin theorem for $N$-continued fraction expansions is shown. More exactly, we obtain a Gauss-Kuzmin theorem related to the natural extension of the measure-dynamical system corresponding to these expansions. Then, using characteristic properties of the transition operator associated with the random system with complete connections underlying $N$-continued fractions on the Banach space of complex-valued functions of bounded variation we derive explicit lower and upper bounds for the convergence rate of the distribution function to its limit.

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Gabriela Ileana Sebe, Dan Lascu. 2017-07-26. A two-dimensional Gauss-Kuzmin theorem for $N$-continued fraction expansions. https://arxiv.org/abs/1707.08393

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