Exponential mixing for the Teichmüller flow
By Artur Avila, S. Gouëzel, J. Yoccoz. 2005
205 citations recorded by the source corpus.
We study the dynamics of the Teichmüller flow in the moduli space of Abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the $SL(2,\mathbb{R})$ action in the moduli space has a spectral gap.
Subfields: Geometry and Topology, Mathematical Physics, Theoretical Computer Science
View Paper: https://www.semanticscholar.org/paper/ae5cc93f03932e8b8570be559c2e0950a1bdf993
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In Geometry and Topology
- Carlos Matheus
- A. Zorich
- G. Forni
- Jayadev S. Athreya
- Corentin Boissy
- Erwan Lanneau
- A. Eskin
- Alexander I. Bufetov
In Mathematical Physics
- Carlos Matheus
- A. Zorich
- G. Forni
- Jayadev S. Athreya
- Corentin Boissy
- Erwan Lanneau
- A. Eskin
- Alexander I. Bufetov
In Theoretical Computer Science
Citations in the corpus
- Dynamics and geometry of the Rauzy–Veech induction for quadratic differentials (2007, methodology): “In this section we introduce the notion of winner and loser, following the terminology of the paper of Avila, Gouezel and Yoccoz [ AGY06 ].”
- Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials (2007, methodology): “This technique was developed and applied in [3, 4, 5, 7, 19, 32], and in other papers; see also surveys [29, 30, 31, 33].”
- Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013, methodology): “In the proof of this result [6], the authors proves firstly that the Teichmüller geodesic flow (i.”
- Quantitative recurrence and large deviations for Teichmüller geodesic flow (2005, methodology): “Avila-Gouezel-Yoccoz [ 1 ] used exponential return estimates to a different family of compact sets to prove the exponential rate of mixing for the Teichmuller geodesic flow, which was the original motivation for this research.”