Badly approximable systems of affine forms, fractals, and Schmidt games
Dynamical Systems
2009-12-30 v2 Number Theory
Abstract
A badly approximable system of affine forms is determined by a matrix and a vector. We show Kleinbock's conjecture for badly approximable systems of affine forms: for any fixed vector, the set of badly approximable systems of affine forms is winning (in the sense of Schmidt games) even when restricted to a fractal (from a certain large class of fractals). In addition, we consider fixing the matrix instead of the vector where an analog statement holds.
Keywords
Cite
@article{arxiv.0912.2445,
title = {Badly approximable systems of affine forms, fractals, and Schmidt games},
author = {Manfred Einsiedler and Jimmy Tseng},
journal= {arXiv preprint arXiv:0912.2445},
year = {2009}
}
Comments
14 pages, typos corrected in the current version