对称平移曲面Veech–McMullen族上的Kontsevich–Zorich共循环

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2017-10-31 DOI:10.3934/JMD.2019002

A. Avila, C. Matheus, J. Yoccoz

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引用次数: 5

摘要

受Veech和McMullen的启发，我们描述了仿射不变轨道折叠上的Kontsevich-Zorich并环，它来自于（循环）覆盖结构。特别地，使用Filip最近的一篇论文中的术语，我们证明了$SU（p，q）$型的Kontsevich-Zorich半群的所有情况都是通过适当的覆盖结构实现的。

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The Kontsevich–Zorich cocycle over Veech–McMullen family of symmetric translation surfaces

We describe the Kontsevich--Zorich cocycle over an affine invariant orbifold coming from a (cyclic) covering construction inspired by works of Veech and McMullen. In particular, using the terminology in a recent paper of Filip, we show that all cases of Kontsevich--Zorich monodromies of $SU(p,q)$ type are realized by appropriate covering constructions.

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来源期刊

Journal of Modern Dynamics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Modern Dynamics (JMD) is dedicated to publishing research articles in active and promising areas in the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research, including: Number theory Symplectic geometry Differential geometry Rigidity Quantum chaos Teichmüller theory Geometric group theory Harmonic analysis on manifolds. The journal is published by the American Institute of Mathematical Sciences (AIMS) with the support of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University.