STNB 2016 (30th edition)
Badly approximable numbers in Diophantine Approximation
Presenters
Abstract
I will talk about two different types of approximation of n-dimensional real vectors: the approximation by rationals, and the approximation by the integer multiples of an arbitrary fixed real vector. In the first case, we talk about classical Diophantine approximation and in the second case we talk about twisted Diophantine approximation. The twisted approximation can easily be interpreted in terms of toral rotations.
I will define the concept of badly approximable numbers in both types of approximations and will discuss the "size" of the sets of badly approximable numbers in R^n and in submanifolds. The problem of determining the size was settled a long time ago for the classical set, whereas it follows from recent results for the twisted set, including recents results by Moshchevitin and myself and Stepanova and myself.
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