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Interval Exchange Transformations and Measured Foliations
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This article is published in Annals of Mathematics.The article was published on 1982-01-01. It has received 851 citations till now. The article focuses on the topics: Interval exchange transformation & Interval (graph theory).read more
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Shadows Of Mapping Class Groups: Capturing Convex Cocompactness
TL;DR: In this paper, the analogy between convex cocompact Kleinian groups and subgroups of the mapping class group of a surface in the sense of B. Farb and L. Mosher was strengthened.
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Weak mixing for interval exchange transformations and translation flows
Artur Avila,Giovanni Forni +1 more
TL;DR: In this paper, the authors show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation, and they also show that the typical translation flow on a surface of genus (g \geq 2 ) with prescribed singularity types is weakly mixed.
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Lyapunov exponents and hodge theory
Maxim Kontsevich,Anton Zorich +1 more
TL;DR: In this paper, a formula connecting characteristic exponents with explicit integrals over moduli spaces of algebraic curves with additional structures was proposed, which can be interpreted as correlators in a topological string theory.
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Dynamics of piecewise isometries
TL;DR: In this article, a systematic study of Euclidean piecewise isometric dynamical systems with a particular focus on the interplay between geometry, symbolic dynamics, and the group of isometries associated with p.i.d.
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Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
Artur Avila,Marcelo Viana +1 more
TL;DR: The Zorich-Kontsevich conjecture on Abelian differentials on compact Riemann surfaces was proved in this paper, which implies the existence of the complete asymptotic Lagrangian flag describing the behavior in homology of the vertical foliation in a typical translation surface.
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Gauss measures for transformations on the space of interval exchange maps
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Quadratic differentials and foliations
John H. Hubbard,Howard Masur +1 more
TL;DR: In this paper, it was shown that the space of measured foliations with the quadratic forms on a fixed Riemann surface is homeomorphic to a sphere, and that the existence of projective classes of foliations is also homeomorphic.