HOROSPHERICAL INVARIANT MEASURES AND A RANK DICHOTOMY FOR ANOSOV GROUPS

Or Landesberg, Minju Lee, Elon Lindenstrauss, Hee Oh

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let G =r i=1 Gi be a product of simple real algebraic groups of rank one and Γ an Anosov subgroup of G with respect to a minimal parabolic subgroup. For each v in the interior of a positive Weyl chamber, let Rv ⊂Γ\G denote the Borel subset of all points with recurrent exp(R+v)-orbits. For a maximal horospherical subgroup N of G, we show that the N-action on Rv is uniquely ergodic if r = rank(G) ≤ 3 and v belongs to the interior of the limit cone of Γ, and that there exists no N-invariant Radon measure on Rv otherwise.

Original languageAmerican English
Pages (from-to)331-362
Number of pages32
JournalJournal of Modern Dynamics
Volume19
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Anosov subgroups
  • Horospherical flow
  • infinite measure rigidity

Fingerprint

Dive into the research topics of 'HOROSPHERICAL INVARIANT MEASURES AND A RANK DICHOTOMY FOR ANOSOV GROUPS'. Together they form a unique fingerprint.

Cite this