2009/12/13 by Einsiedler, Manfred, Tseng, Jimmy
#11K60 #37A17 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.0912.2445
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.