Limits of geodesic push-forwards of horocycle invariant measures

DOI10.1017/etds.2020.87zbMath1490.37006arXiv1908.11037OpenAlexW3093582489WikidataQ114119084 ScholiaQ114119084MaRDI QIDQ5005958

Giovanni Forni

Publication date: 12 August 2021

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.11037

zbMATH Keywords

Birkhoff ergodic theoremOseledets multiplicative ergodic theorempointwise equidistributionTeichmüller horocycle flow

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Ergodic theorems, spectral theory, Markov operators (37A30) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Group actions on manifolds and cell complexes in low dimensions (57M60) Teichmüller theory for Riemann surfaces (30F60) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (2)

Polynomial effective equidistribution ⋮ On convergence of random walks on moduli space

Cites Work

• Semisimplicity and rigidity of the Kontsevich-Zorich cocycle
• Every flat surface is Birkhoff and Oseledets generic in almost every direction
• Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
• Siegel measures
• Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
• Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
• Asymptotic formulas on flat surfaces
• Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group
• Nondivergence of horocyclic flows on moduli space
• Pointwise equidistribution and translates of measures on homogeneous spaces
• Lyapunov spectrum of invariant subbundles of the Hodge bundle

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