Workshop: Ergodic Theory and Geometry

研讨会旨在提供一个国际论坛，讨论混沌动力系统的统计性质、几何和量子混沌之间的最新发展。它将特别侧重于鼓励研究人员之间的相互作用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，不如采用统计的观点并试图理解典型的行为，这样会更有成效。在这个层面上，混沌系统表现出相当多的结构，并且在过去几年中在理解这方面取得了很大进展。这表现在相关性衰减、统计极限律、不变测度分类、渐近公式等现象中。这个领域对混沌系统的量子理论有直接的应用。

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.