The dynamics of the Weil-Petersson flow

DOI10.1007/978-3-319-43059-1_6zbMATH Open1442.37005arXiv1601.00690OpenAlexW2779756304MaRDI QIDQ1642186

Carlos Matheus

Publication date: 20 June 2018

Abstract: This text grew out of some lecture notes prepared by the author in the occasion of a series of three lectures during the workshop "Young mathematicians in dynamical systems" organized by Francoise Dal'bo, Louis Funar, Boris Hasselblatt and Barbara Schapira in November 2013 at CIRM, Marseille, France. The three lectures at the origin of this text were part of a minicourse by Keith Burns, Boris Hasselblatt and the author around the recent theorem of Burns-Masur-Wilkinson on the ergodicity of the Weil-Petersson (WP) geodesic flow. The goal of these notes is the same of the author's lectures: we cover some of the aspects related to moduli spaces of Riemann surfaces (and Teichmueller theory) in the Burns-Masur-Wilkinson's proof of the ergodicity of WP flow.

Full work available at URL: https://arxiv.org/abs/1601.00690

zbMATH Keywords

ergodicityTeichmüller theorymoduli spaces of Riemann surfacesWeil-Petersson geodesic flowBurns-Masur-Wilkinson theorem

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Teichmüller theory for Riemann surfaces (30F60) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Teichmüller theory; moduli spaces of holomorphic dynamical systems (37F34)

Related Items (3)

The dynamics of generic Kuperberg flows ⋮ Weyl-flow and the conformally symplectic structure of thermostatted billiards: the problem of the hyperbolicity ⋮ \(W\)-flows on Weyl manifolds and Gaussian thermostats

Recommendations

• Unnamed Item 👍 👎
• Unnamed Item 👍 👎
• Dissipative Euler flows and Onsager's conjecture 👍 👎
• Topological dynamics of the Weil-Petersson geodesic flow 👍 👎
• The transverse dynamics of a holomorphic flow 👍 👎
• Ergodicity of the Weil-Petersson geodesic flow 👍 👎
• The dynamics of the flow for prescribed harmonic mean curvature 👍 👎
• The dynamics of generic Kuperberg flows 👍 👎
• Dynamical properties of the Weil-Petersson metric 👍 👎
• Weingarten flows in Riemannian manifolds 👍 👎

This page was built for publication: The dynamics of the Weil-Petersson flow