{"title":"Cascades in the Dynamics of Measured Foliations","authors":"C. McMullen","doi":"10.24033/ASENS.2237","DOIUrl":null,"url":null,"abstract":"This paper studies the behavior of harmonic measured foliations on compact Riemann surfaces. Cascades in the dynamics of such a foliation can occur as its relative periods are varied. We show that in the case of genus 2, the bifurcation locus arising from such a variation is a closed, countable set of R that embeds in ω. Resume Nous etudions le comportement des feuilletages mesures harmoniques sur les surfaces de Riemann compactes. Quands les periodes relatives varient, on peut observer des cascades dans la dynamique d’un tel feuilletage. Dans le cas du genre 2, on montre que le lieu de bifurcation resultant d’une telle variation est un sous-ensemble denombrable et ferme de R, qui se plonge dans ω.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"28 1","pages":"1-39"},"PeriodicalIF":1.3000,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Scientifiques De L Ecole Normale Superieure","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/ASENS.2237","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 22
Abstract
This paper studies the behavior of harmonic measured foliations on compact Riemann surfaces. Cascades in the dynamics of such a foliation can occur as its relative periods are varied. We show that in the case of genus 2, the bifurcation locus arising from such a variation is a closed, countable set of R that embeds in ω. Resume Nous etudions le comportement des feuilletages mesures harmoniques sur les surfaces de Riemann compactes. Quands les periodes relatives varient, on peut observer des cascades dans la dynamique d’un tel feuilletage. Dans le cas du genre 2, on montre que le lieu de bifurcation resultant d’une telle variation est un sous-ensemble denombrable et ferme de R, qui se plonge dans ω.
研究了紧致黎曼曲面上谐波测量叶理的行为。在这种叶理作用的动力学中，随着相对周期的变化，会发生级联。我们证明了在属2的情况下，由这种变异引起的分岔轨迹是嵌入在ω中的一个封闭的、可数的R集合。在黎曼紧致曲面上的谐波测量的一致性。量子数周期相对变化，但观察者的级联性和动力学不一致。Dans le cas du genre 2，在montre que le lieu de分叉上产生的d 'une tellle变异是sous-ensemble可命名为et ferme de R, quise plonge Dans ω。
期刊介绍：
The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics.
Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition.
The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.
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