@article{d23f660dd2ff49a5858de12e53329d85,
title = "Badly approximable vectors on fractals",
abstract = "For a large class of closed subsets C of ℝn, we show that the intersection of C with the set of badly approximable vectors has the same Hausdorff dimension as C. 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.",
author = "Dmitry Kleinbock and Barak Weiss",
note = "Funding Information: ACKNOWLEDGEMENT: This research was supported by BSF grant 2000247 and NSF Grant DMS-0239463. We are grateful to Hillel Furstenberg and Mariusz Urbanski for helpful discussions, and to Yuval Peres and Sanju Velani for telling us of different approaches to these problems. We benefited greatly from many discussions with Elon Lindenstrauss during our work on [KLW], in which some of the results of this paper were announced.",
year = "2005",
month = dec,
day = "1",
doi = "10.1007/BF02772538",
language = "English",
volume = "149",
pages = "137--170",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Springer New York",
}