teichm曲线的模符号

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-12 DOI:10.1515/crelle-2021-0019

C. McMullen

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引用次数: 7

摘要

摘要本文引入了一个附加于任意双曲黎曼曲面V上的非abel模符号𝒮(V){{\mathcal{S}}(V)}空间，并应用它得到了关于多边形台球和全纯1型的新结果。特别地，它证明了正多边形中台球周期轨迹的刻痕行为是由一组同胚于ωω+1{\ ω ^{\ ω}+1}的可数测度控制的。

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Modular symbols for Teichmüller curves

Abstract This paper introduces a space of nonabelian modular symbols 𝒮⁢(V){{\mathcal{S}}(V)} attached to any hyperbolic Riemann surface V, and applies it to obtain new results on polygonal billiards and holomorphic 1-forms. In particular, it shows the scarring behavior of periodic trajectories for billiards in a regular polygon is governed by a countable set of measures homeomorphic to ωω+1{\omega^{\omega}+1}.

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来源期刊

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.