Diophantine Properties of Measures and Homogeneous Dynamics
نویسنده
چکیده
This is a survey of the so-called “quantitative nondivergence” approach to metric Diophantine approximation developed approximately 10 years ago in my collaboration with Margulis. The goal of this paper is to place the theory of approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on Rn. The correspondence between multidimensional Diophantine approximation and dynamics of lattices in Euclidean spaces is discussed in an elementary way, and several recent results obtained by means of this correspondence are surveyed.
منابع مشابه
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...
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