Logarithm laws for flows on homogeneous spaces

  title={Logarithm laws for flows on homogeneous spaces},
  author={Dmitry Kleinbock and G. A. Margulis},
  journal={Inventiones mathematicae},
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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We prove analogues of the logarithm laws of Sullivan and Kleinbock-Margulis in the context of unipotent flows. In particular, we obtain results for one-parameter actions on the space of lattices
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ec 2 00 6 A logarithm law for automorphism groups of trees Sa ’ ar Hersonsky
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Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
  • K. Schmidt
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1981
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Ergodic Theory and Semisimple Groups
1. Introduction.- 2. Moore's Ergodicity Theorem.- 3. Algebraic Groups and Measure Theory.- 4. Amenability.- 5. Rigidity.- 6. Margulis' Arithmeticity Theorems.- 7. Kazhdan's Property (T).- 8. Normal
Discrete Subgroups of Semisimple Lie Groups
1. Statement of Main Results.- 2. Synopsis of the Chapters.- 3. Remarks on the Structure of the Book, References and Notation.- 1. Preliminaries.- 0. Notation, Terminology and Some Basic Facts.- 1.