A gauss-kuzmin theorem and related questions for $θ$-expansions

Gabriela Ileana Sebe; Dan Lascu

doi:10.1155/2014/980461

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arXiv · 1305.5563

A gauss-kuzmin theorem and related questions for $θ$-expansions

Gabriela Ileana Sebe·Dan Lascu

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Abstract

Using the natural extension for $θ$-expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotients of these expansions. Together with the ergodic behavior of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.

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Gabriela Ileana Sebe, Dan Lascu. 2013-05-23. A gauss-kuzmin theorem and related questions for $θ$-expansions. https://doi.org/10.1155/2014%2F980461

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