Treffer: A transfer property in Diophantine approximation

The author investigates the well-known link between the properties of uniform simultaneous rational approximations for a vector \(w\) in \(\mathbb{R}^n\) and the sequence of best simultaneous rational approximations for such a vector \(w\). The study makes use of a dynamical framework. In particular, the quality of the best simultaneous rational approximations to the vector \(w\) is expressed in terms of the best return times near the origin for the translation \(x\mapsto x+ w\) on the \(n\)-dimensional torus.