Teichmueller flow and Weil-Petersson flow

2015/05/05 by Ursula Hamenstaedt, Hamenstaedt, Ursula · 1 citation
Mathematics · #30F60 #37C15 #37C40 #37D40 #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1505.01113

openalex publication_date 2015/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a non-exceptional oriented surface S let Q(S) be the moduli space of area one quadratic differentials. We show that there is a Borel subset E of Q(S) which is invariant under the Teichmueller flow F^t and of full measure for every invariant Borel probability measure, and there is a measurable conjugacy of the restriction of F^t to E into the Weil-Petersson flow. This conjugacy induces a continuous injection H of the space of invariant Borel probability measures for F^t into the space of invariant Borel probability measures for the Weil-Petersson flow. The map H is not surjective, but its image contains the Lebesgue Liouville measure.

Citations

• Train tracks and the Gromov boundary of the complex of curves

Cited by

• Rates of mixing for the Weil-Petersson geodesic flow II: exponential\n mixing in exceptional moduli spaces

Related

• Bowen's construction for the Teichmueller flow
• Bernoulli measures for the Teichmueller flow
• Dynamical properties of the Weil-Petersson metric
• Symbolic dynamics for the Teichmueller flow
• Dynamics of the Teichmueller flow on compact invariant sets