Bad is null
Number Theory
2023-07-20 v1 Dynamical Systems
Abstract
In this paper we develop a general framework of badly approximable points in a metric space equipped with a -finite doubling Borel regular measure . We establish that under mild assumptions the -measure of the set of badly approximable points is always zero. The framework can be applied to a variety of settings in Diophantine approximation and dynamical systems, which we also consider, including weighted and -arithmetic Diophantine approximations, Diophantine approximation on manifolds and intrinsic approximations on fractals.
Cite
@article{arxiv.2307.10109,
title = {Bad is null},
author = {Victor Beresnevich and Shreyasi Datta and Anish Ghosh and Benjamin Ward},
journal= {arXiv preprint arXiv:2307.10109},
year = {2023}
}