Workshop: Ergodic Theory and Geometry

研讨会：遍历理论与几何

• 批准号: EP/F037805/1
• 负责人: Richard Sharp
• 金额: $ 2.09万
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FF037805%2F1
• 关键词: Workshop; Ergodic; Theory; Geometry

The workshop aims to provide an international forum to discuss the latest developments on the interface between statistical properties of chaotic dynamical systems, geometry, and quantum chaos. It will be particularly focused on encouraging interactions between researchers and the transfer of methods between different topics, aimed at facilitating further progress.Chaotic dynamical systems have an extremely complicated orbit structure. Rather than trying to understand every orbit, it is more fruitful to adopt a statistical viewpoint and try to understand typical behaviour. At this level, chaotic sysyems exhibit a considerable amount of structure and there has been great progress in understanding this over the last few years. This manifests itself in such phenomena as decay of correlations, statistical limit laws, classification of invariant measures, asymptotic formulae. The area has immediate applications to the quantum theory of chaotic systems.

该研讨会旨在提供一个国际论坛，讨论混沌动力系统，几何和量子混沌的统计特性之间的接口的最新发展。它将特别侧重于鼓励研究人员之间的互动和不同主题之间的方法转移，旨在促进进一步的进展。混沌动力系统具有极其复杂的轨道结构。与其试图理解每一个轨道，不如采用统计学的观点，并试图理解典型的行为。在这个层次上，混沌系统表现出相当多的结构，在过去的几年里，对这一点的理解有了很大的进展。这表现在这样的现象，如衰减的相关性，统计极限定律，分类不变的措施，渐近公式。该领域直接应用于混沌系统的量子理论。