Hyperbolic Dynamics, Large Deviations and Fluctuations

这笔赠款将为参加为期一学期的“双曲线动力学、大偏差和波动”项目的两个讲习班的美国学员提供差旅支持，该项目于2013年3月至6月在瑞士洛桑理工学院伯努利中心举行。第一个工作坊是关于“大偏差和热力学形式”，第二个工作坊是关于“动力系统的极限定理”。在每个研讨会之前，都有一系列针对研究生和博士后的小型强化课程，由动力系统领域的杰出数学家讲授。在过去的50年里，动力系统的统计性质一直是动力学中广泛研究的中心，在数学的其他领域以及物理、工程和生物之外都有许多重要的应用。对统计性质的系统研究始于60年代初的S和西奈和鲁埃尔，后来又是鲍恩的工作，他奠定了热力学的基础。尽管他们开发的方法具有相当一般的性质，但它们的应用大多限于一致双曲组。非均匀双曲性理论，也被称为“佩辛理论”的发展，为我们打开了更广阔的视野。如今动力学的主要活动集中在研究非一致双曲型系统、具有奇点的双曲型系统，以及更广泛地说，具有某种双曲性的系统不属于前面提到的范畴。该计划的主要目的是将从事动力系统统计性质及其在统计力学和数学物理中的应用的领先专家和年轻研究人员聚集在一起，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主题工作的各国数学家提供一个活动重点和一个聚会场所。它们将为年轻和成熟的研究人员提供一个论坛，与世界各地的同行交流想法，促进当前和未来的研究，并为几个方面的进一步研究制定具体的议程。所有参与者，包括传统上代表人数不足的群体的成员，也将受益于许多来自欧洲的强大的年轻数学家的出席。

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.