Parabolic perturbations of unipotent flows on compact quotients of \(\mathrm{SL}(3,\mathbb{R})\)

DOI10.1007/s00220-019-03348-0zbMath1436.37005arXiv1711.04821OpenAlexW2963095113MaRDI QIDQ2326898

Davide Ravotti

Publication date: 10 October 2019

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.04821

zbMATH Keywords

Haar measureunipotent flowsMautner phenomenonsmooth perturbations

Mathematics Subject Classification ID

Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Measurable group actions (22F10) Homogeneous flows (37A17)

Related Items (4)

Polynomial mixing for time-changes of unipotent flows ⋮ New time-changes of unipotent flows on quotients of Lorentz groups ⋮ Slow chaos in surface flows ⋮ Mixing for smooth time-changes of general nilflows

Cites Work

• Unnamed Item
• Unnamed Item
• Invariant distributions for homogeneous flows and affine transformations
• Mixing for the time-changes of Heisenberg nilflows
• Time-changes of horocycle flows
• Spectral analysis of time changes of horocycle flows
• The first cohomology of parabolic actions for some higher-rank abelian groups and representation theory
• Cohomological equation and cocycle rigidity of parabolic actions in some higher-rank Lie groups
• Rigidity of time changes for horocycle flows
• Invariant measures and minimal sets of horospherical flows
• On measure rigidity of unipotent subgroups of semisimple groups
• On Raghunathan's measure conjecture
• Mixing of all orders of Lie groups actions
• Ergodic properties of horocycle flows on surfaces of negative curvature
• The horocycle flow is mixing of all degrees
• Invariant measures for actions of unipotent groups over local fields on homogeneous spaces
• First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
• Invariant distributions and time averages for horocycle flows
• Strict measure rigidity for unipotent subgroups of solvable groups
• Orbit closures of generic unipotent flows on homogeneous spaces of \(SL(3,{\mathbb{R}})\)
• Raghunathan's conjectures for Cartesian products of real and \(p\)-adic Lie groups
• Kakutani equivalence of unipotent flows
• Cocycles over higher-rank abelian actions on quotients of semisimple Lie groups
• Absolutely continuous spectrum for parabolic flows/maps
• Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions
• Flows on Homogeneous Spaces: A New Look
• Mixing for suspension flows over skew-translations and time-changes of quasi-abelian filiform nilflows
• Riemannian geometry

This page was built for publication: Parabolic perturbations of unipotent flows on compact quotients of \(\mathrm{SL}(3,\mathbb{R})\)