On badly approximable numbers

Abstract

Motivated by a wonderful paper by Ngoc Ai Van Nguyen, Anthony Poëls and Damien Roy, where a powerful method was introduced, we prove a criterion for a vector $\alpha \in {\mathbb{R}}^d$ to be a badly approximable vector. Moreover we construct certain examples which show that a more general version of our criterion is not valid.

minor correction after refereeing

References in corpus (1)

• On Schmidt and Summerer parametric geometry of numbers