Vol. 8, No. 1, 2019

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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 2 such that the set

Badθ :={(η1,η2) : inf xx12 max i=1,2xθi ηi > 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