Logarithm laws for flows on homogeneous spaces

@article{Kleinbock1999LogarithmLF,
  title={Logarithm laws for flows on homogeneous spaces},
  author={Dmitry Kleinbock and G. A. Margulis},
  journal={Inventiones mathematicae},
  year={1999},
  volume={138},
  pages={451-494}
}
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… 
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