Flows on homogeneous spaces and Diophantine approximation on manifolds

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We present a new approach to metric Diophantine approximation on manifolds based on the correspondence between approximation properties of numbers and orbit properties of certain flows on homogeneous spaces. This approach yields a new proof of a conjecture of Mahler, originally settled by V. Sprindzhuk in 1964. We also prove several related hypotheses of A. Baker and V. Sprindzhuk formulated in 1970s. The core of the proof is a theorem which generalizes and sharpens earlier results on non-divergence of unipotent flows on the space of lattices.
19 pages. To appear in Annals of Mathematics

Keywords

Number Theory, Dynamical Systems, 11J13, 11J83; 22E99, 57S25

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/77511

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9810036
 http://arxiv.org/abs/math/9810036
 Ann. Math. 148 (1998), 339--360.

Collections

arXiv