English

Badly Approximable Systems of Affine Forms and Incompressibility on Fractals

Number Theory 2013-07-12 v1

Abstract

We explore and refine techniques for estimating the Hausdorff dimension of exceptional sets and their diffeomorphic images. Specifically, we use a variant of Schmidt's game to deduce the strong C^1 incompressibility of the set of badly approximable systems of linear forms as well as of the set of vectors which are badly approximable with respect to a fixed system of linear forms.

Keywords

Cite

@article{arxiv.1208.2091,
  title  = {Badly Approximable Systems of Affine Forms and Incompressibility on Fractals},
  author = {Ryan Broderick and Lior Fishman and David Simmons},
  journal= {arXiv preprint arXiv:1208.2091},
  year   = {2013}
}