Hyperbolic Dynamics, Large Deviations and Fluctuations

这笔赠款是为两个研讨会的美国参与者提供旅行支持，这两个研讨会是为期一个学期的计划“双曲线动力学，大偏差和波动”的一部分，该计划将于2013年3月至6月在瑞士洛桑的伯努利理工学院中心举行。第一个研讨会是关于“大偏差和数学形式主义”，第二个是关于“动力系统的极限定理”。每个研讨会之前，由杰出的数学家在动力系统领域的研究生和博士后学生一系列密集的迷你课程。在过去的50年中，动力系统的统计性质一直是动力学广泛研究的中心，在数学的其他领域以及物理学，工程学和生物学之外都有许多重要的应用。对统计性质的系统研究始于60年代早期，由西奈和吕埃尔以及后来奠定热力学基础的鲍恩的工作开始。虽然他们开发的方法是相当普遍的性质，其应用主要限于一致双曲系统。非均匀双曲性理论（也称为“Pesin理论”）的发展为我们打开了更广阔的视野。这些天在动力学的主要活动集中在研究非一致双曲系统，双曲系统的奇异性，更一般地说，系统的某些种类的双曲性，但不属于前面提到的类别。该计划的主要目的是汇集领先的专家和年轻的研究人员致力于动力系统的统计特性及其在统计力学和数学物理中的应用，并促进学术交流和合作。这些讲习班的目的是为从事动力系统和相关专题工作的各国数学家提供一个活动重点和聚会场所。它们将成为年轻和成熟的研究人员与世界各地的同行交流思想的论坛，促进当前和未来的研究，并为若干领域的进一步研究制定具体议程。所有与会者，包括传统上代表性不足的群体的成员也将受益于来自欧洲的许多强大的年轻数学家的存在。

This grant is to provide travel support for American participants of two Workshops organized as part of a semester-long program "Hyperbolic Dynamics, Large Deviations and Fluctuations" that takes place at the Centre Interfacultaire Bernoulli, Ecole Politechnique, Lausanne, Switzerland, March-June 2013. The first workshop is on "Large deviations and thermodynamical formalism" and the second one is on "Limit Theorems for dynamical systems". Each workshop is preceded by a series of intensive mini-courses for post-graduate and post-doctoral students given by distinguished mathematicians in the field of dynamical systems. During the last 50 years statistical properties of dynamical systems have been a center of extensive study in dynamics with many great applications to other areas of mathematics as well as outside to physics, engineering and biology. The systematic study of statistical properties began in the early 60's with the works of Sinai and Ruelle, and later of Bowen, who laid the foundations of thermodynamics. Though the methods they developed were of rather general nature, their applications were restricted mostly to uniformly hyperbolic systems. Much wider horizons were opened after the development of non-uniform hyperbolicity theory that is also known as "Pesin's theory". The main activities in dynamics these days are concentrated around studying non-uniformly hyperbolic systems, hyperbolic systems with singularities, and more generally, systems which posses some kind of hyperbolicity however do not belong to the previously mentioned categories. The main aim of the program is to bring together leading experts and young researchers working on statistical properties of dynamical systems and their applications in statistical mechanics, and mathematical physics as well as to foster scholarly exchange and collaboration. The workshops are intended to provide a focus of activities and a meeting place for mathematicians from various countries working in dynamical systems and related topics. They will serve as a forum for both young and established researchers to exchange ideas with their counterparts throughout the world, promote current and future research and create a concrete agenda for further research on several fronts. All participants, including members of traditionally underrepresented groups will also benefit from the presence of many strong young mathematicians from Europe.