Hausdorff dimension OF dynamical Dophantine approximation associated with ergodic mixing systems

2025/02/18 by Daviaud, E. · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2502.13051

Abstract

In this article, we estimate the Hausdorff dimension of dynamical coverings with respect to mixing ergodic systems. More precisely, if the ergodic measure is exact-dimensionnal, we establish a formula provided that the system is polynomially fast mixing and if the measure is not exact-dimensionnal, we establish a similar result under super-polynomial speed of mix assumpetion. As an application of our result, we extend the result of Fan-Shmeling-Troubetzkoy for the doubling map on the circle to the case of the times 2, times 3 map on the two dimensional torus.

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• Dynamical covering sets in self-similar sets

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