# Flows on homogeneous spaces and Diophantine approximation on manifolds

@article{Kleinbock1998FlowsOH, title={Flows on homogeneous spaces and Diophantine approximation on manifolds}, author={Dmitry Kleinbock and G. A. Margulis}, journal={Annals of Mathematics}, year={1998}, volume={148}, pages={339-360} }

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. G. Sprindzuk in 1964. We also prove several related hypotheses of Baker and Sprindzuk formulated in 1970s. The core of the proof is a theorem which generalizes and sharpens earlier results on nondivergence…

## 337 Citations

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