On ε-escaping trajectories in homogeneous spaces

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Let G/Γ be a finite volume homogeneous space of a semisimple Lie group G, and {exp(tD)} be a one-parameter Ad-diagonalizable subgroup inside a simple Lie subgroup G0 of G. Denote by Zε,D the set of points x ∈ G/Γ whose {exp(tD)}-trajectory has an escape for at least an ε-portion of mass along some subsequence. We prove that the Hausdorff codimension of Zε,D is at least cε, where c depends only on G, G0 and Γ.

Original languageEnglish (US)
Pages (from-to)329-357
Number of pages29
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number1
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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