Sets of inhomogeneous linear forms can be not isotropically winning
Copyright policy ) Dyakova, Natalia;
Sets of inhomogeneous linear forms can be not isotropically winning
We give an example of irrational vector $\pmb�� \in \mathbb{R}^2$ such that the set $Bad_{\pmb��} := \{(��_1,��_2): \inf_{x\in\mathbb{N}} x^{\frac{1}{2}} \max_{i=1,2} \|x ��_i-��_i\|>0\}$ is not absolutely winning with respect to McMullen's game.
13 pages, 2 figures
- Lomonosov Moscow State University Russian Federation
inhomogeneous diophantine approximation, Mathematics - Number Theory, inhomogeneous Diophantine approximation, winning sets, FOS: Mathematics, 11J20, Number Theory (math.NT), 11J13, Inhomogeneous linear forms
inhomogeneous diophantine approximation, Mathematics - Number Theory, inhomogeneous Diophantine approximation, winning sets, FOS: Mathematics, 11J20, Number Theory (math.NT), 11J13, Inhomogeneous linear forms
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