# Winning Sets, Quasiconformal Maps and Diophantine Approximation

 Title: Winning Sets, Quasiconformal Maps and Diophantine Approximation Author: McMullen, Curtis T. Citation: McMullen, Curtis, T. 2010. Winning sets, quasiconformal maps and diophantine approximation. Geometric and Functional Analysis 20(3): 726-740. Full Text & Related Files: winning_sets.pdf (208.5Kb; PDF) Abstract: This paper describes two new types of winning sets in $$\mathbb{R}^n$$, defined using variants of Schmidt’s game. These strong and absolute winning sets include many Diophantine sets of measure zero and first category, and have good behavior under countable intersections. Most notably, they are invariant under quasiconformal maps, while classical winning sets are not. Published Version: doi:10.1007/s00039-010-0078-3 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9918805 Downloads of this work: