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arXiv · 1711.06280

Sets of inhomogeneous linear forms can be not isotropically winning

Natalia Dyakova
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Abstract

We give an example of irrational vector $\pmbθ \in \mathbb{R}^2$ such that the set $Bad_{\pmbθ} := \{(η_1,η_2): \inf_{x\in\mathbb{N}} x^{\frac{1}{2}} \max_{i=1,2} \|x θ_i-η_i\|>0\}$ is not absolutely winning with respect to McMullen's game.

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Natalia Dyakova. 2017-11-16. Sets of inhomogeneous linear forms can be not isotropically winning. https://doi.org/10.2140/moscow.2019.8.3

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