2021/08/15 by Valérie Berthé, Jungwon Lee, Berthé, Valérie +1 · 1 citation
Mathematics · Physics and Astronomy · #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2108.06780
openalex publication_date 2021/08/15 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We present a dynamical and spectral study of Ostrowski's map based on the use\nof transfer operators. The Ostroswki dynamical system is obtained as a\nskew-product of the Gauss map (it has the Gauss map as a base and interval\nfibers) and produces expansions of real numbers with respect to an irrational\nbase given by continued fractions. By studying spectral properties of the\nassociated transfer operator, we show that the Ostroswki dynamical system\nadmits an absolutely continuous invariant measure with piecewise holomorphic\ndensity and exponential mixing properties. We deduce a central limit theorem\nfor associated random variables of an arithmetic nature and motivated by\napplications in inhomogeneous Diophantine approximation, we get Bowen--Ruelle\ntype implicit estimates in terms of spectral elements for the Hausdorff\ndimension of a certain bounded digit set.\n