Nikolay G. Moshchevitin

Khintchine's singular Diophantine systems and their applications

This paper is a survey of classical and recent methods in Diophantine approximation theory and its applications related to Khintchines results on the existence of real numbers admitting extremely good approximations by rational numbers. Bibliography: 145 titles.

Badly approximable numbers and Littlewood-type problems

We establish that the set of pairs

Colorings of the space ℝn with several forbidden distances

(alpha, beta)

Distribution of values of linear functions and asymptotic behavior of trajectories of some dynamical systems

of real numbers such that

Recurrence of the integral of a smooth three-frequency conditionally periodic function

liminf_{q to + infty} q cdot (log q)^2 cdot Vert q alpha Vert cdot Vert q beta Vert > 0,

A note on weighted badly approximable linear forms.

where

Best simultaneous approximations: Norms, signatures, and asymptotic directions

Vert cdot Vert

On Kleinbock's Diophantine result

denotes the distance to the nearest integer, has full Hausdorff dimension in