Diophantine approximation on subspaces of ${\mathbb{R}}^n$ and dynamics on homogeneous spaces

Abstract

In recent years, the ergodic theory of group actions on homogeneous spaces has played a significant role in the metric theory of Diophantine approximation. We survey some recent developments with special emphasis on Diophantine properties of affine subspaces and their submanifolds.

Survey article. To appear in the Handbook of Group Actions Vol III/IV, Editors Lizhen Ji, Athanase Papadopoulos, Shing-Tung Yau

References in corpus (1)

• Badly approximable points on manifolds

Cited by in corpus (2)

• Diophantine approximation on lines in ${\mathbb{C}}^2$ with Gaussian prime constraints
• Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced version