STNB 2016 (30è any)
Badly approximable numbers in Diophantine Approximation
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I will talk about two different types of approximation of n-dimensional real vectors: the approximation by rationals, and the approximation by the integer orbit 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 talk about the "size" of these sets. For the classical set, the problem of working out the size was settled a long time ago, whereas it follows from recent results for the twisted set, particularly from a recent result by Moshchevitin and myself.
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