Flows on Homogeneous Spaces
نویسندگان
چکیده
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 ows on homogeneous spaces. This approach yields a new proof of a conjecture of Mahler, originally settled by V. G. Sprind zuk in 1964. We also prove several related hypotheses of Baker and Sprind zuk formulated in 1970s. The core of the proof is a theorem which generalizes and sharpens earlier results on non-divergence of unipotent ows on the space of lattices.
منابع مشابه
Flows on Homogeneous Spaces and Diophantine Approximation on Manifolds
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. Sprindžuk in 1964. We also prove several related hypotheses of Baker and Sprindžuk formulated in 1970...
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