Badly Approximable Systems of Affine Forms and Incompressibility on Fractals
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 C1 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.
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