HAUSDORFF DIMENSION of the SET APPROXIMATED by IRRATIONAL ROTATIONS

Let θ be an irrational number and φ:N → R⁺ be a monotone decreasing function tending to zero. Let [Equation presented here] i.e. the set of points which are approximated by the irrational rotation with respect to the error function φ(n). In this article, we give a complete description of the Hausdorff dimension of E_φ(θ) for any monotone function φ and any irrational θ.