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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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Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum ℋ(1,1)
TL;DR: In this paper , the authors studied the horocycle flow on strata of translation surfaces, introduced new invariants for ergodic measures, and analyzed the interaction of the horcycle flow and real Rel surgeries.
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The Finsler geometry of the Teichmüller metric
Weixu Su,Youliang Zhong +1 more
TL;DR: In this article, a brief survey of some results on the Finsler structures of Teichmuller metric is presented, mainly focusing on the connection between holomorphic quadratic differentials and extremal length of measured foliations.
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Masur-Veech volume of the gothic locus
TL;DR: In this article, the Masur-Veech volume of the gothic locus was calculated based on the Euler characteristics of the Teichmuller curve.
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Some arithmetical aspects of renormalization in Teichmüller dynamics: On the occasion of Corinna Ulcigrai winning the Brin Prize
TL;DR: In this paper , the authors present some works of Corinna Ulcigrai closely related to Diophantine approximations and generalizing classical notions to the context of interval exchange maps, translation surfaces and Teichmüller dynamics.
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Journal ArticleDOI
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.