VEECH GROUPS, IRRATIONAL BILLIARDS AND STABLE ABELIAN DIFFERENTIALS

Ferran Valdez

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VEECH GROUPS, IRRATIONAL BILLIARDS AND STABLE ABELIAN DIFFERENTIALS

机译：教育群体，理性的台词和稳定的阿贝尔语差异

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摘要

We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we prove that these groups are non-discrete subgroups of SO(2,R) and we calculate their rank.

机译：我们描述了由不合理的成角度的多边形台球或不可约的稳定阿贝尔微分产生的平坦表面的Veech群。对于不合理的多边形台球，我们证明这些组是SO（2，R）的非离散子组，并计算它们的等级。

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来源
《Discrete and continuous dynamical systems》 |2012年第3期|p.1055-1063|共9页
作者
Ferran Valdez;
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作者单位

Centro de Ciencias Matematicas UNAM, Campus Morelia, C.P. 58089 Morelia, Michoacan, Mexico;

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原文格式 PDF
正文语种 eng
中图分类
关键词
polygonal billiards; veech group;

机译：多边形台球veech集团;

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1. Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials [J] . Chen Dawei, Moeller Martin, Sauvaget Adrien, Inventiones Mathematicae . 2020,第1期

机译：雅典差分模型空间的Masur-veeech卷和交汇处
2. Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories [J] . L.N.C. Adamson, A.H. Osbaldestin Physica, D. Nonlinear phenomena . 2014,第Null期

机译：屏障台球中相关性的重新归一化：二次非理性轨迹
3. Ergodicity and quantum correlations in irrational triangular billiards [J] . T. Araujo Lima, S. Rodrıguez-Perez, F. M. de Aguiar PHYSICAL REVIEW E . 2013,第6期

机译：无理三角台球的遍历性和量子相关性
4. Vehicle Smart Grid Allocation using Multi-Agent Systems sensitive to Irrational Behavior and Unstable Power Supply [C] . Joao Tiago Aparicio, Miguel Trinca, Daniel Castro, Iberian Conference on Information Systems and Technologies . 2021

机译：车辆智能电网分配使用对非理性行为和不稳定电源敏感的多种子体系统
5. Zero-Cycles and Measures of Irrationality for Abelian Varieties [D] . Martin, Olivier. 2020

机译：ZEALIAN品种的零周期和非理性措施
6. Differentials of Functions with Arguments and Values in Topological Abelian Groups [O] . A. D. Michal 1940

机译：拓扑阿贝尔群中带有参数和值的函数微分
7. VEECH GROUPS, IRRATIONAL BILLIARDS AND STABLE ABELIAN DIFFERENTIALS [O] . Ferrán Valdez 2011

机译：VEECH团队，不合理的法案和稳定的aBELIaN差异
8. Intrinsic Heights of Stable Varieties. Application to Abelian Varieties [R] . Bost, J. B. 1994

机译：稳定品种的内在高度。适用于阿贝尔品种

VEECH GROUPS, IRRATIONAL BILLIARDS AND STABLE ABELIAN DIFFERENTIALS

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