Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

摘要

The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in R-n akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978) [2], Dodson, Dickinson (2000) [18] and Beresnevich, Bernik, Kleinbock, Margulis (2002) [8]. In the case of planar curves, the complete Hausdorff dimension theory is developed.