Schmidt’s game on fractals

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The set of badly approximable vectors is strongly C1 incompressible (2011, background): “The following lemma, proved in [12] and adapted from Schmidt [26], gives a condition on a set K allowing one to estimate from below the Hausdorff dimension of S ∩ K for every S which is winning on K.”
Badly approximable systems of affine forms, fractals, and Schmidt games (2009, background): “in Schmidt’s proof of the winning property, and the more recent proofs of L. Fishman ([8] and [ 9 ]) involving the intersection of Bad0(m; n) with certain fractals.”
Badly approximable points on manifolds (2013, background): “As alreadymentioned, the setsBad(r) and even their restrictions to naturally occurring fractals have been investigated in higher dimensions, see [26,34– 36].”