Badly Approximable Systems of Affine Forms and Incompressibility on   Fractals
  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. 
Ryan Broderick, Lior Fishman and David Simmons
math.NT