Journal ArticleDOI
Gauss measures for transformations on the space of interval exchange maps
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This article is published in Annals of Mathematics.The article was published on 1982-03-01. It has received 778 citations till now. The article focuses on the topics: Interval exchange transformation & Gauss.read more
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Connected components of the moduli spaces of Abelian differentials with prescribed singularities
Maxim Kontsevich,Anton Zorich +1 more
TL;DR: In this article, the moduli space of pairs (C,ω) is considered, 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 zeros.
Journal ArticleDOI
Connected components of the moduli spaces of Abelian differentials with prescribed singularities
Maxim Kontsevich,Anton Zorich +1 more
TL;DR: In this paper, the moduli space of pairs (C,w) where C is a smooth compact complex curve of a given genus and w is a holomorphic 1-form on C with a given list of multiplicities of zeros was considered.
Rational billiards and flat structures
Howard Masur,Serge Tabachnikov +1 more
TL;DR: In this paper, the authors show that rational billiards can be used to determine a flat surface in rational polygons and interval exchange maps in quadratic differentials in the unit square.
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Ergodicity of billiard flows and quadratic differentials
TL;DR: On considere un systeme billard de 2 objets de masses m 1 and m 2, on montre que pour un ensemble dense de paires (m 1,m 2 ) ce systeme est ergodique.
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Non-ergodic interval exchange transformations
Michael Keane,Michael Keane +1 more
TL;DR: In this article, the authors construct interval exchange transformations on four intervals satisfying a strong irrationality condition and having exactly two ergodic invariant probability measures, and show that the Weyl equidistribution theorem is false even under the strongest irrationality assumptions.