On a Gauss-Kuzmin Type Problem for a Family of Continued Fractions

2010/10/23 by Dan Lascu, Lascu, Dan
Mathematics · #11J70 #11K50 #28D05 #60A10 #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1010.4864

openalex publication_date 2010/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a family of continued fraction expansion of reals from the unit interval. The Perron-Frobenius operator of the transformation which generates this expansion under the invariant measure of this transformation is given. Using the ergodic behavior of homogeneous random system with complete connections associated with this expansion we solve a variant of Gauss-Kuzmin problem for this continued fraction expansion.

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