The Weil-Petersson geodesic flow is ergodic

DOI10.4007/annals.2012.175.2.8zbMath1254.37005arXiv1004.5343OpenAlexW2962817192WikidataQ101223189 ScholiaQ101223189MaRDI QIDQ410116

Keith Burns, Amie Wilkinson, Howard A. Masur

Publication date: 17 April 2012

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.5343

zbMATH Keywords

Riccati equationsergodicitygeodesic flownegative curvatureWeil-Peterssonincomplete Riemannian manifoldssingular and nonuniform hyperbolicity

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Teichmüller theory for Riemann surfaces (30F60) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items

Cusp excursions of random geodesics in Weil-Petersson type metrics, Hodge and Teichmüller, Hyperbolic systems, zeta functions and other friends, On the Weil-Petersson convex geometry of Teichmüller space, The vanishing rate of Weil-Petersson sectional curvatures, Equiboundedness of the Weil-Petersson metric, Riemann moduli spaces are quantum ergodic, Spectral theory for the Weil-Petersson Laplacian on the Riemann moduli space, Rates of mixing for the Weil-Petersson geodesic flow: exponential mixing in exceptional moduli spaces, Rates of mixing for the Weil-Petersson geodesic flow. I: No rapid mixing in non-exceptional moduli spaces, Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms, Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities, Symbolic dynamics for non-uniformly hyperbolic systems, Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces, Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards, Weil-Petersson geodesics on the modular surface

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