The horocycle flow is mixing of all degrees

DOI10.1007/BF01390274zbMath0395.28012OpenAlexW2091682375MaRDI QIDQ1252956

Brian Marcus

Publication date: 1978

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142560

zbMATH Keywords

ManifoldBorel MeasureErgodic Translation FlowG-Invariant MeasureHomogeneous SpaceHorocycle FlowKolmogorov AutomorphismsMeasure Preserving FlowMixing of All DegreesSemisimple Lie GroupStationary PointsSurface of Constant Negative Curvature and Finite Area

Mathematics Subject Classification ID

One-parameter continuous families of measure-preserving transformations (28D10)

Related Items (26)

Dynamics over Teichmüller space ⋮ Mutual isomorphisms of translations of a homogeneous flow ⋮ Quantitative multiple mixing ⋮ The Cartesian square of the horocycle flow is not loosely Bernoulli ⋮ Polynomial 3-mixing for smooth time-changes of horocycle flows ⋮ Asymptotics and limit theorems for horocycle ergodic integrals à la Ratner (with an appendix by Emilio Corso) ⋮ Almost sure convergence of the multiple ergodic average for certain weakly mixing systems ⋮ Invariant distributions and time averages for horocycle flows ⋮ Higher Order Correlations for Group Actions ⋮ A connection between the mixing properties of a flow and the isomorphism entering into its transformations ⋮ Stochastic intertwinings and multiple mixing of dynamical systems ⋮ Mixing of all orders of Lie groups actions ⋮ On the self-similarity problem for smooth flows on orientable surfaces ⋮ Disjointness of Moebius from Horocycle Flows ⋮ Factors of horocycle flows ⋮ Slow chaos in surface flows ⋮ Quantitative equidistribution of horocycle push-forwards of transverse arcs ⋮ Mixing for smooth time-changes of general nilflows ⋮ Multiple mixing for a class of conservative surface flows ⋮ Predictive sets ⋮ Approximate identities and Lagrangian Poincaré recurrence ⋮ Horocycle flows are loosely Bernoulli ⋮ Parabolic perturbations of unipotent flows on compact quotients of \(\mathrm{SL}(3,\mathbb{R})\) ⋮ On the self-similarity problem for Gaussian-Kronecker flows ⋮ Commutator methods for the spectral analysis of uniquely ergodic dynamical systems ⋮ A class of multipliers for \({\mathcal W}^\perp\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unique ergodicity of the horocycle flow: variable negative curvature case
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Kolmogorov Automorphisms on Homogeneous Spaces
• Ergodicity of Flows on Homogeneous Spaces

This page was built for publication: The horocycle flow is mixing of all degrees