TY - JOUR
T1 - On ε-escaping trajectories in homogeneous spaces
AU - Rodriguez Hertz, Federico
AU - Wang, Zhiren
N1 - Funding Information:
2020 Mathematics Subject Classification. 37A17, 37D40, 11L55. Key words and phrases. Escaping trajectories, Hausdorff dimension, homogeneous spaces, di- agonal flow, homogeneous dynamics. F.R.H. was supported by NSF grant DMS-1900778. Z.W. was supported by NSF grant DMS-1753042.
Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.
PY - 2021/1
Y1 - 2021/1
N2 - 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.
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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U2 - 10.3934/dcds.2020365
DO - 10.3934/dcds.2020365
M3 - Article
AN - SCOPUS:85096799268
VL - 41
SP - 329
EP - 357
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
SN - 1078-0947
IS - 1
ER -