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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2011, Issue 660


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

Manfred Einsiedler / Jimmy Tseng
Published Online: 2011-06-16 | DOI: https://doi.org/10.1515/crelle.2011.078


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.

About the article

Received: 2009-12-30

Revised: 2010-08-11

Published Online: 2011-06-16

Published in Print: 2011-11-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2011, Issue 660, Pages 83–97, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2011.078.

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