## 677 Citations

Large genus asymptotics for volumes of strata of abelian differentials

- MathematicsJournal of the American Mathematical Society
- 2020

<p>In this paper we consider the large genus asymptotics for Masur-Veech volumes of arbitrary strata of Abelian differentials. Through a combinatorial analysis of an algorithm proposed in 2002 by…

Mixing Flows on Moduli Spaces of Flat Bundles over Surfaces

- MathematicsGeometry and Physics: Volume II
- 2018

This chapter extends Teichmüller dynamics to a flow on the total space of a flat bundle of deformation spaces of representations of the fundamental group of a fixed surface S in a Lie group G. The…

Minimality of interval exchange transformations with restrictions

- Mathematics
- 2017

It is known since a 40-year-old paper by M.Keane that minimality is a generic (i.e., holding with probability one) property of an irreducible interval exchange transformation. If one puts some…

Square-tiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata

- Mathematics
- 2016

We prove that square-tiled surfaces having fixed combinatorics of horizontal cylinder decomposition and tiled with smaller and smaller squares become asymptotically equidistributed in any ambient…

The Hölder property for the spectrum of translation flows in genus two

- Mathematics
- 2015

The paper is devoted to generic translation flows corresponding to Abelian differentials with one zero of order two on flat surfaces of genus two. These flows are weakly mixing by the Avila–Forni…

Cohomology classes represented by measured foliations, and Mahler's question for interval exchanges

- Mathematics
- 2011

A translation surface on (S, \Sigma) gives rise to two transverse measured foliations \FF, \GG on S with singularities in \Sigma, and by integration, to a pair of cohomology classes [\FF], \, [\GG]…

Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow

- Mathematics
- 2010

We study a diophantine property for translation surfaces, defined in term of saddle connections and inspired by the classical theorem of Khinchin. We prove that the same dichotomy holds as in…

The Distribution of Gaps for Saddle Connection Directions

- Mathematics
- 2010

Motivated by the study of billiards in polygons, we prove fine results for the distribution of gaps of directions of saddle connections on translation surfaces. As an application we prove that for…

Limit theorems for translation flows

- Mathematics
- 2008

The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem…

N ov 2 00 5 Riemann surfaces : noncommutative story

- Mathematics
- 2008

For an open and dense subset in the Teichmüller space, we introduce a coordinate system which is (relatively) well-behaved under the action of the mapping class group. Surprisingly, the coordinates…

## References

SHOWING 1-9 OF 9 REFERENCES

Projective Swiss Cheeses and Uniquely Ergodic Interval Exchange Transformations

- Mathematics
- 1981

1. Introduction. Recall that an interval exchange on a finite (left closed-right open) interval, J ⊆ ℝ is a transformation, T, of J which results from decomposing J into a finite number of (left…

Quadratic differentials and foliations

- Mathematics
- 1979

This paper concerns the interplay between the complex structure of a Riemann surface and the essentially Euclidean geometry induced by a quadratic differential. One aspect of this geometry is the "…

Non-ergodic interval exchange transformations

- Mathematics
- 1977

We construct interval exchange transformations on four intervals satisfying a strong irrationality condition and having exactly two ergodic invariant probability measures. This shows that although…