On ε-escaping trajectories in homogeneous spaces

Federico Rodriguez Hertz; Zhiren Wang

doi:10.3934/dcds.2020365

On ε-escaping trajectories in homogeneous spaces

Federico Rodriguez Hertz
, Zhiren Wang

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 Z_ε,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 Z_ε,D is at least cε, where c depends only on G, G₀ and Γ.

Original language	English (US)
Pages (from-to)	329-357
Number of pages	29
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	41
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2020365
State	Published - Jan 2021

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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AB - 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.

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On ε-escaping trajectories in homogeneous spaces

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