Dilation surfaces and their Veech groups

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2019-03-29 DOI:10.3934/JMD.2019005

E. Duryev, C. Fougeron, Selim Ghazouani

引用次数: 8

Abstract

We introduce a class of objects which we call 'dilation surfaces'. These provide families of foliations on surfaces whose dynamics we are interested in. We present and analyze a couple of examples, and we define concepts related to these in order to motivate several questions and open problems. In particular we generalize the notion of Veech group to dilation surfaces, and we prove a structure result about these Veech groups.

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扩张面及其Veech基团

我们介绍了一类物体，我们称之为“膨胀曲面”。这些提供了我们感兴趣的表面上的叶理家族的动力学。我们提出并分析了几个例子，并定义了与这些相关的概念，以激发几个问题和悬而未决的问题。特别地，我们将Veech群的概念推广到扩张曲面，并证明了这些Veech群在结构上的一个结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.