TY - JOUR
T1 - Badly approximable systems of affine forms, fractals, and Schmidt games
AU - Einsiedler, Manfred
AU - Tseng, Jimmy
PY - 2011/11
Y1 - 2011/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80755167801&partnerID=8YFLogxK
U2 - 10.1515/CRELLE.2011.078
DO - 10.1515/CRELLE.2011.078
M3 - Article (Academic Journal)
AN - SCOPUS:80755167801
SN - 0075-4102
VL - 660
SP - 83
EP - 97
JO - Journal für die reine und angewandte Mathematik
JF - Journal für die reine und angewandte Mathematik
ER -