Reflection Groups and Discrete Dynamical Systems

反射群和离散动力系统

• 批准号: DP160101728
• 负责人: Prof Nalini Joshi
• 金额: $ 34.92万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP160101728
• 关键词: Reflection; Groups; Discrete; Dynamical; Systems

This project aims to solve long-standing problems in discrete dynamical systems that are of particular interest to physics, by using reflection groups to reveal unexpected geometric insights. Mathematics has the power to abstract crucial patterns from complex observations. Symmetries familiar in the real world, like the hexagonal patterns of honeycombs, arise inside convoluted structures in high-dimensional systems. By revealing the structure of space-filling polytopes in integrable systems, the project seeks to find sought-after reductions of high-dimensional discrete models to two dimensions. Expected outputs include new reductions to discrete Painlevé equations, new circle patterns useful for computer graphics and discrete holomorphic functions.

该项目旨在通过使用反射组揭示意外的几何见解来解决物理学特别感兴趣的离散动态系统中的长期问题。数学有能力从复杂的观察结果中抽象至关重要的模式。在现实世界中熟悉的对称性，例如蜂窝的六角形模式，在高维系统中的复杂结构内出现。通过揭示可集成系统中空间填充多型的结构，该项目旨在找到将高维离散模型减少到两个维度之后的感觉。预期的输出包括对离散painlevé方程的新减少，对计算机图形有用的新圆形模式和离散的全态函数。