arXiv subjects

Natalia Dyakova

Publications and source records attributed to Natalia Dyakova.

2 recordsLinked to original sources

arXiv2019

On badly approximable subspaces

Given an $a$-dimensional linear subspace $\mathfrak{A}$ in $\mathbb{R}^d$ which contains a badly approximable $b$-dimensional subspace $\mathfrak{B} \subset \mathfrak{A}$. We study the badly approximability almost all $c$-dimensional linear subspaces $\mathfrak{C} \subset \mathfrak{A}$.

math.NT↗

arXiv2017

Sets of inhomogeneous linear forms can be not isotropically winning

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.

math.NT↗