Flows on homogeneous spaces and Diophantine approximation on manifolds
Abstract
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 nondivergence of unipotent flows on the space of lattices.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1998
 DOI:
 10.48550/arXiv.math/9810036
 arXiv:
 arXiv:math/9810036
 Bibcode:
 1998math.....10036K
 Keywords:

 Number Theory;
 Dynamical Systems;
 11J13;
 11J83;
 22E99;
 57S25
 EPrint:
 19 pages. To appear in Annals of Mathematics