Non-dense orbits on homogeneous spaces and applications to geometry and number theory

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Ergodic Theory on Homogeneous Spaces and Metric Number Theory

Article outline This article gives a brief overview of recent developments in metric number theory, in particular, Diophantine approximation on manifolds, obtained by applying ideas and methods coming from dynamics on homogeneous spaces. Glossary 1. Definition: Metric Diophantine approximation 2. Basic facts 3. Introduction 4. Connection with dynamics on the space of lattices 5. Diophantine app...

Equidistribution in Homogeneous Spaces and Number Theory

We survey some aspects of homogeneous dynamics — the study of algebraic group actions on quotient spaces of locally compact groups by discrete subgroups. We give special emphasis to results pertaining to the distribution of orbits of explicitly describable points, especially results valid for the orbits of all points, in contrast to results that characterize the behavior of orbits of typical po...

Dynamics of Subgroup Actions on Homogeneous Spaces of Lie Groups and Applications to Number Theory

Diagonalizable flows on locally homogeneous spaces and number theory

We discuss dynamical properties of actions of diagonalizable groups on locally homogeneous spaces, particularly their invariant measures, and present some number theoretic and spectral applications. Entropy plays a key role in the study of theses invariant measures and in the applications. Mathematics Subject Classification (2000). 37D40, 37A45, 11J13, 81Q50.