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… 

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