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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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The flow group of rooted abelian or quadratic differentials
TL;DR: In this paper, the flow group of any component of any stratum of rooted abelian or quadratic differentials (those marked with a horizontal separatrix) is defined as the group generated by almost-flow loops.
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Simple closed geodesics on hyperelliptic translation surfaces.
TL;DR: In this article, the maximal number of disjoint and nonhomotopic closed geodesics which do not contain singularities for translation surfaces in the hyperelliptic components was given.
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Energy functions on moduli spaces of flat surfaces with erasing forest
TL;DR: In this article, it was shown that the integral of the energy functions mentioned above with respect to this volume form is finite, and the authors used this result to recover some classical results due to Masur-Veech, and Thurston.
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On the combinatorial structure of Rauzy graphs
TL;DR: The main result of as mentioned in this paper is that the graph R(π) of a permutation π ∈ Sm0 is a tree composed of cycles if any simple cycle in this graph consists of edges of the same type.
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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.