Quantitative recurrence and large deviations for Teichmüller geodesic flow

By Jayadev S. Athreya. 2005

65 citations recorded by the source corpus.

We prove quantitative recurrence and large deviations results for the Teichmuller geodesic flow on connected components of strata of the moduli space Qg of holomorphic unit-area quadratic differentials on a compact genus g ≥ 2 surface.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f76dce9c8afb7a2194209076a68c651389a0d9e

How researchers see this paper

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In Applied Mathematics

1. J. Yoccoz
2. Artur Avila
3. Matt Bainbridge
4. S. Gouëzel
5. Marcelo Viana
6. A. Zorich
7. Bassam Fayad
8. David Damanik

In Geometry and Topology

1. J. Yoccoz
2. Artur Avila
3. Matt Bainbridge
4. S. Gouëzel
5. A. Zorich
6. G. Forni
7. Carlos Matheus
8. Ian Melbourne

In Mathematical Physics

1. Artur Avila
2. J. Yoccoz
3. S. Gouëzel
4. A. Zorich
5. Matt Bainbridge
6. Marcelo Viana
7. G. Forni
8. Carlos Matheus

Citations in the corpus

• Euler characteristics of Teichmüller curves in genus two (2006, background): “8 is a corollary of the main result in Athreya’s thesis [3].”
• Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow (2010, methodology): “Since µ is SL(2 , R )-invariant, Athreya’s Theorem [Ath06] shows the existence of a compact set K in X/ Γ such that, under the iteration of g t , µ -almost every point spends asymptotically at least half its time in K .”
• Exponential mixing for the Teichmüller flow (2005, background): “Tt(x, ai) is of the form (x � , 0). Indeed, since r is uniformly bounded from below by a constant e1 ,t here are at most r(x) e1 + 1 such points. At each of these points,”