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 language | American English |
---|---|
Pages (from-to) | 331-362 |
Number of pages | 32 |
Journal | Journal of Modern Dynamics |
Volume | 19 |
DOIs | |
State | Published - 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