Sets of inhomogeneous linear forms can be not isotropically winning

Dyakova, Natalia

doi:10.2140/moscow.2019.8.3

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Sets of inhomogeneous linear forms can be not isotropically winning

Natalia Dyakova

Vol. 8 (2019), No. 1, 3–13

DOI: 10.2140/moscow.2019.8.3

Abstract

We give an example of irrational vector $θ \in ℝ^{2}$ such that the set

{Bad}_{θ} : = {(η_{1}, η_{2}) : inf_{x \in ℕ} x^{1 ∕ 2} max_{i = 1, 2} ∥ x θ_{i} - η_{i} ∥ > 0}

is not absolutely winning with respect to McMullen’s game.

Keywords

inhomogeneous diophantine approximation, winning sets

Mathematical Subject Classification 2010

Primary: 11J13

Milestones

Received: 1 December 2017

Published: 11 August 2018

Authors

Natalia Dyakova
Department of Mathematics and Mechanics Moscow State University Moscow Russia

Vol. 8, No. 1, 2019