Badly approximable systems of affine forms, fractals, and Schmidt games

Manfred Einsiedler*, Jimmy Tseng

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)

Abstract

A badly approximable system of affine forms is determined by a matrix and a vector. We show Kleinbock's conjecture for badly approximable systems of affine forms: for any fixed vector, the set of badly approximable systems of affine forms is winning (in the sense of Schmidt games) even when restricted to a fractal (from a certain large class of fractals). In addition, we consider fixing the matrix instead of the vector where an analog statement holds.

Original languageEnglish
Pages (from-to)83-97
Number of pages15
JournalJournal für die reine und angewandte Mathematik
Volume660
DOIs
Publication statusPublished - Nov 2011

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