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arXiv · 1709.07187

On convergence rate in the Gauss-Kuzmin problem for $\theta$-expansions

Gabriela Ileana Sebe·Dan Lascu
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Abstract

After providing an overview of $\theta$-expansions introduced by Chakraborty and Rao, we focus on the Gauss-Kuzmin problem for this new transformation. Actually, we complete our study on these expansions by proving a two-dimensional Gauss-Kuzmin theorem. More exactly, we obtain such a theorem related to the natural extension of the associated measure-dynamical system. Finally, we derive explicit lower and upper bounds of the error term which provide interesting numerical calculations for the convergence rate involved.

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Gabriela Ileana Sebe, Dan Lascu. 2017-09-21. On convergence rate in the Gauss-Kuzmin problem for $\theta$-expansions. https://arxiv.org/abs/1709.07187

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