Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow

By A. Eskin, M. Kontsevich, A. Zorich. Publications mathématiques (Bures-sur-Yvette), 2011

178 citations recorded by the source corpus.

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/55bbd3bdfbd210ddc4de5ef5e18dfa23905c99dd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Carlos Matheus
2. Martin Möller
3. Martin Moeller
4. G. Forni
5. Dawei Chen
6. J. Yoccoz
7. Don Zagier
8. Corentin Boissy

In Mathematical Physics

1. Martin Möller
2. Carlos Matheus
3. Martin Moeller
4. Dawei Chen
5. J. Yoccoz
6. G. Forni
7. Don Zagier
8. Corentin Boissy

In Statistical and Nonlinear Physics

1. Carlos Matheus
2. G. Forni
3. Martin Möller
4. Martin Moeller
5. J. Yoccoz
6. Dawei Chen
7. Corentin Boissy
8. Don Zagier

Citations in the corpus

• Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013, methodology): “Here, the study of the geometry of translation surfaces near the boundary of the moduli spaces (and the regularity assumption on the probability measure μ in the statement) plays a crucial role in the proof that the boundary term is given by the Siegel–Veech constant c(μ) and this completes this cru”
• Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials (2019, background): “[12]) and connection to Lyapunov exponents [15] is the second variant.”
• CONNECTED COMPONENTS OF THE STRATA OF THE MODULI SPACE OF MEROMORPHIC DIFFERENTIALS (2012, background): “Eskin, Kontsevich and Zorich show in a recent paper [6] that when a sequence of Abelian differentials .”
• A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (2013, methodology): “The sum of the nonnegative exponents for Masur-Veech measures can be computed explicitly from Siegel-Veech constants [EKZ].”
• Quasimodularity and large genus limits of Siegel-Veech constants (2016, methodology): “A second proof is given in Section 4, which is more algebraic and uses the main result of [13] relating the area Siegel-Veech constant to the sum of Lyapunov exponents.”