A gauss-kuzmin theorem and related questions for $\theta$-expansions

Gabriela Ileana Sebe; Dan Lascu

doi:10.1155/2014/980461

A gauss-kuzmin theorem and related questions for $\theta$-expansions

Number Theory 2014-05-16 v1 Dynamical Systems

Authors: Gabriela Ileana Sebe , Dan Lascu

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Abstract

Using the natural extension for $\theta$ -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.

Keywords

Gauss-Kuzmin theorem $\theta$-expansions incomplete quotients infinite-order chain ergodic behavior random system with complete connections

Cite

@article{arxiv.1305.5563,
  title  = {A gauss-kuzmin theorem and related questions for $\theta$-expansions},
  author = {Gabriela Ileana Sebe and Dan Lascu},
  journal= {arXiv preprint arXiv:1305.5563},
  year   = {2014}
}

Comments

27 pages

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