Journal ArticleDOI
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
Citations
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On the geometry and dynamics of diffeomorphisms of surfaces
TL;DR: In this paper, the authors presented a proof of the classification of surface automorphisms from the point of view of Teichmüller theory, generalizing Teichmiiller's theorem by allowing the Riemann surface to vary as well as the map.
Journal ArticleDOI
Geometry of the complex of curves I: Hyperbolicity
Howard Masur,Yair N. Minsky +1 more
TL;DR: The complex of curves on a surface as mentioned in this paper is a simplicial complex whose vertices are homotopy classes of simple closed curves, and simplices are sets of classes which can be realized disjointly.
Journal ArticleDOI
Gauss measures for transformations on the space of interval exchange maps
Journal ArticleDOI
Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
TL;DR: In this article, an asymptotic formula for the length spectrum of the billiard in isosceles triangles with angles (π/n, π /n,n−2/nπ) was given for the uniform distribution of infinite billiard trajectories in the same triangles.
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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.
References
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Journal ArticleDOI
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.
Book
Ergodic theory: Introductory lectures
TL;DR: In this paper, the authors propose a measure-preserving transformation with pure point spectrum and topological entropy, and show that it is invariant to spectral invariants and isomorphism.
Journal ArticleDOI
A “minimal”, non-uniquely ergodic interval exchange transformation
Harvey B. Keynes,Dan Newton +1 more
Book ChapterDOI
Projective Swiss Cheeses and Uniquely Ergodic Interval Exchange Transformations
TL;DR: In this article, 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 subintervals and translating these subinterval in such a way that their union is again J.