Hausdorff dimension OF dynamical Dophantine approximation associated with ergodic mixing systems
Dynamical Systems
2025-10-13 v3 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2502.13051,
title = {Hausdorff dimension OF dynamical Dophantine approximation associated with ergodic mixing systems},
author = {E. Daviaud},
journal= {arXiv preprint arXiv:2502.13051},
year = {2025}
}