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arXiv · 1208.2091

Badly Approximable Systems of Affine Forms and Incompressibility on Fractals

Ryan Broderick·Lior Fishman·David Simmons
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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.

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Ryan Broderick, Lior Fishman, David Simmons. 2012-08-10. Badly Approximable Systems of Affine Forms and Incompressibility on Fractals. https://arxiv.org/abs/1208.2091

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