Badly approximable vectors on fractals

Dmitry Kleinbock, Barak Weiss

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

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.

Original languageEnglish
Pages (from-to)137-170
Number of pages34
JournalIsrael Journal of Mathematics
Volume149
DOIs
StatePublished - 1 Dec 2005

Fingerprint

Dive into the research topics of 'Badly approximable vectors on fractals'. Together they form a unique fingerprint.

Cite this