Abstract
For a large class of closed subsetsC of ℝn, we show that the intersection ofC with the set of badly approximable vectors has the same Hausdorff dimension asC. The sets are described in terms of measures they support. Examples include (but are not limited to) self-similar sets such as Cantor’s ternary sets or attractors for irreducible systems of similarities satisfying Hutchinson’s open set condition.
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Kleinbock, D., Weiss, B. Badly approximable vectors on fractals. Isr. J. Math. 149, 137–170 (2005). https://doi.org/10.1007/BF02772538
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DOI: https://doi.org/10.1007/BF02772538