Asymptotic formulas on flat surfaces

By A. Eskin, H. Masur. Ergodic Theory and Dynamical Systems, 2001

175 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/537c34976aebfa0113591a62c97e0b22cae4ffe4

How researchers see this paper

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

In Computational Theory and Mathematics

1. A. Zorich
2. Dawei Chen
3. Jayadev S. Athreya
4. G. Forni
5. A. Wright
6. Martin Möller
7. Don Zagier
8. Martin Moeller

In Mathematical Physics

1. A. Zorich
2. Martin Möller
3. Dawei Chen
4. A. Eskin
5. G. Forni
6. Martin Moeller
7. A. Wright
8. Jayadev S. Athreya

Citations in the corpus

• Exponential mixing for the Teichmüller flow (2005, background): “[ EM ]), there exists a constant C > 0 such that”
• Cylinder deformations in orbit closures of translation surfaces (2013, background): “Background For an introduction to translation surfaces, see the surveys by Masur and Tabachnikov [14] and Zorich [30].”
• Chapter 8 - On the Lyapunov Exponents of the Kontsevich–Zorich Cocycle (2006, background): “These numbers are conjecturally related to the Siegel–Veech constants which arise in counting problems for embedded flat cylinders or saddle-connections on translation surfaces [42,13].”
• A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (2013, unknown): “Moreover, from the work of Eskin and Masur [16], there exists for each ε > 0 a compact set Kε ⊂ C such that ν(Kε) > 1 − ε for any such probability measure ν.”
• Multiple Saddle Connections on Flat Surfaces and the Principal Boundry of the Moduli Spaces of Quadratic Differentials (2008, background): “It is easy to see that the set VC(S) satisfies axioms (A), (B), (Cµ) in [ EM ].”
• Quasimodularity and large genus limits of Siegel-Veech constants (2016, methodology): “The fundamental results of Veech and Eskin-Masur ([44], [14]) jointly imply that for appropriate V and ν there is a constant c(ν, V ), such that for all functions χ we have 1 ν(H) ∫ H χ̂dν = c(ν, V ) ∫ R2 χdxdy.”
• Quantitative recurrence and large deviations for Teichmüller geodesic flow (2005, methodology): “Let Lθ = ν(Uθ). The following lemma is proved in [ 8 ].”
• Euler characteristics of Teichmüller curves in genus two (2006, background): “The volume of is an interesting quantity, which according to Veech [80] and Eskin and Masur [21] gives information about the dynamics of the geodesic flow of a generic Abelian differential .”
• Moduli spaces of Abelian differentials: The principal boundary, counting problems, and the Siegel–Veech constants (2002, methodology): “Remark 3.2. The issue of higher multiplicity and specifying the angles is not explicitly addressed in [ EMa ].”