Badly approximable vectors on fractals

Dmitry Kleinbock, Barak Weiss

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


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.

Original languageEnglish
Pages (from-to)137-170
Number of pages34
JournalIsrael Journal of Mathematics
StatePublished - 1 Dec 2005

ASJC Scopus subject areas

  • General Mathematics


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