## Connected components of the moduli spaces of Abelian differentials with prescribed singularities

- M. Kontsevich, A. Zorich
- Mathematics
- 29 January 2002

Consider the moduli space of pairs (C,ω) where C is a smooth compact complex curve of a given genus and ω is a holomorphic 1-form on C with a given list of multiplicities of zeroes. We describe… Expand

## LYAPUNOV EXPONENTS AND HODGE THEORY

- M. Kontsevich, A. Zorich
- Mathematics
- 28 January 1997

We started from computer experiments with simple one-dimensional ergodic dynamical systems called interval exchange transformations. Correlators in these systems decay as a power of time. In the… Expand

## Moduli spaces of Abelian differentials: The principal boundary, counting problems, and the Siegel–Veech constants

A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment… Expand

## Finite Gauss measure on the space of interval exchange transformations

- A. Zorich
- Mathematics
- 1996

© Annales de l’institut Fourier, 1996, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions… Expand

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

- A. Eskin, M. Kontsevich, A. Zorich
- Mathematics
- 26 December 2011

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… Expand

## Flat Surfaces

- A. Zorich
- Mathematics
- 14 September 2006

Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a… Expand

## Deviation for interval exchange transformations

- A. Zorich
- MathematicsErgodic Theory and Dynamical Systems
- 1 December 1997

Consider a long piece of a trajectory $x, T(x), T(T(x)), \ldots, T^{n-1}(x)$ of an interval exchange transformation $T$. A generic interval exchange transformation is uniquely ergodic. Hence, the… Expand

## Square Tiled Surfaces and Teichmüller Volumes of the Moduli Spaces of Abelian Differentials

- A. Zorich
- Mathematics
- 2002

We present an approach for counting the Teichmuller volumes of the moduli spaces of Abelian differentials on a Riemann surface of genus g. We show that the volumes can be counted by means of counting… Expand

## Lyapunov spectrum of square-tiled cyclic covers

- A. Eskin, M. Kontsevich, A. Zorich
- Mathematics
- 29 July 2010

A cyclic cover over the Riemann sphere branched at four points inherits a natural flat structure from the "pillow" flat structure on the basic sphere. We give an explicit formula for all individual… Expand

## SQUARE-TILED CYCLIC COVERS

- G. Forni, C. Matheus, A. Zorich
- Mathematics
- 24 July 2010

A cyclic cover of the complex projective line branched at four
appropriate points has a natural structure of a square-tiled surface.
We describe the combinatorics of such a square-tiled surface,… Expand

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