Logarithm laws for flows on homogeneous spaces View Full Text


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Article Info

DATE

1999-12

AUTHORS

D.Y. Kleinbock, G.A. Margulis

ABSTRACT

In this paper we generalize and sharpen D. Sullivan’s logarithm law for geodesics by specifying conditions on a sequence of subsets {At | t∈ℕ} of a homogeneous space G/Γ (G a semisimple Lie group, Γ an irreducible lattice) and a sequence of elements ft of G under which #{t∈ℕ | ftx∈At} is infinite for a.e. x∈G/Γ. The main tool is exponential decay of correlation coefficients of smooth functions on G/Γ. Besides the general (higher rank) version of Sullivan’s result, as a consequence we obtain a new proof of the classical Khinchin-Groshev theorem on simultaneous Diophantine approximation, and settle a conjecture recently made by M. Skriganov. More... »

PAGES

451-494

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s002220050350

DOI

http://dx.doi.org/10.1007/s002220050350

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1016687602


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