HOROSPHERICAL INVARIANT MEASURES AND A RANK DICHOTOMY FOR ANOSOV GROUPS

Or Landesberg, Minju Lee, Elon Lindenstrauss, Hee Oh

Research output: Contribution to journalArticlepeer-review

1 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

Funding Information:
Received September 15, 2021; revised October 31, 2022. 2020 Mathematics Subject Classification: Primary: 37A17, 37A40, 22E40; Secondary: 22F30. Key words and phrases: Horospherical flow, Anosov subgroups, infinite measure rigidity. OL: Partially supported by ISF-Moked grant 2095/19. EL: Partially supported by ERC 2020 grant no. 833423. HO: Partially supported by the NSF grant 0003086.

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