Rates of mixing for the Weil–Petersson geodesic flow: exponential mixing in exceptional moduli Spaces

Keith Burns, Howard Masur, Carlos Matheus, Amie Wilkinson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We establish exponential mixing for the geodesic flow φt: T1S→ T1S of an incomplete, negatively curved surface S with cusp-like singularities of a prescribed order. As a consequence, we obtain that the Weil–Petersson flows for the moduli spaces M1 , 1 and M0 , 4 are exponentially mixing, in sharp contrast to the flows for Mg , n with 3 g- 3 + n> 1 , which fail to be rapidly mixing. In the proof, we present a new method of analyzing invariant foliations for hyperbolic flows with singularities, based on changing the Riemannian metric on the phase space T1S and rescaling the flow φt.

Original languageEnglish (US)
Pages (from-to)240-288
Number of pages49
JournalGeometric and Functional Analysis
Volume27
Issue number2
DOIs
StatePublished - Apr 1 2017

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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