Sets of inhomogeneous linear forms can be not isotropically winning

Abstract

We give an example of irrational vector θ θ θ ∈ R 2 such that the set Bad θ θ θ :not absolutely winning with respect to McMullen's game. * Supported by RFBR and RNF grant. arXiv:1711.06280v1 [math.NT] 16 Nov 2017 [21] J. Tseng, Badly approximable affine forms and Schmidt games, J. Number Theory 129 (2009), 3020-3025.