Conference on "Global Dynamics Beyond Uniform Hyperbolicity"

该提案要求资助美国与会者参加将于2013年5月27日至6月7日在波兰贝德勒沃的巴拿赫中心举行的“超越均匀双曲性的全球动力学”会议。这次会议是自2001年以来举行的一系列国际会议中的第六次，其中两次在美国举行，主要由国家科学基金会资助。会议将集中于可微动力系统的整体定性研究（拓扑和遍历），特别是非一致双曲的微分同态和向量场。主要内容包括：-超越双曲性：部分双曲性，非一致双曲性，奇异双曲性，李雅普诺夫指数，维数，统计性质。-全局和半局部性质：c1拓扑，分岔。-其他主题：区间动力学，叶理。这种对光滑动力系统的研究起源于早期建立太阳系稳定性的努力。早期的先驱如亨利·庞加莱和乔治·伯克霍夫发现了稳定和不稳定的机制，从而开始了双曲动力系统的研究。大约在同一时间，几何学家埃伯哈德·霍普夫（Eberhard Hopf）用双曲方法研究了负弯曲空间（如以闵可夫斯基空间为模型的空间）中测地线（直线）的长期行为。一个世纪后，双曲动力系统的研究已经发展成为一个成熟的领域，是动力学的基石之一。这次会议是每隔几年举行一次的系列会议之一，汇集了代表五大洲的真正的国际专家小组，探讨超越双曲线的最新发展。通过这些研讨会接触到这一前沿工作，推动了上一代美国研究生的研究进步，他们中的许多人将在本次研讨会上发言。这个研讨会之前的化身也导致了国际合作团队，我们预计未来会有类似性质的好处。

This proposal requests funding for US-based participants to attend the conference "Global Dynamics Beyond Uniform Hyperbolicity" which will be held at the Banach Center in Bedlewo, Poland May 27- June 7, 2013. This conference is sixth in a series of international conferences held since 2001, two of which were held in the US and funded primarily by the NSF. The conference will focus on the global qualitative study (topological and ergodic) of differentiable dynamical systems, especially diffeomorphisms and vector fields, that are not uniformly hyperbolic. Among the main topics to be covered are:-Beyond Hyperbolicity: Partial hyperbolicity, Nonuniform hyperbolicity, Singular hyperbolicity, Lyapunov exponents, Dimension, Statistical properties.-Global and Semilocal Properties: The C1-topology, Bifurcations.-Other Topics: Interval Dynamics, Foliations.This study of smooth dynamical systems has its origins in early efforts to establish the stability of the solar system. Early pioneers such as Henri Poincare and George Birkhoff discovered mechnanisms for stability and instability, thus initiating the study of hyperbolic dynamical systems. Around the same time, the geometer Eberhard Hopf used hyperbolic methods to study the long-term behavior of geodesics (straight lines) in negatively curved spaces (such as those modelled on Minkowski space). A century later, the study of hyperbolic dynamical systems has blossomed into a mature field, one of the cornerstones of dynamics. This conference, one in a series held every few years, brings together a truly international group of experts, representing 5 continents, to explore the latest developments beyond hyperbolicity. Exposure to this cutting edge work through these workshops has spurred research advances in a previous generation of US graduate students, many of whom will speak at this workshop. Previous incarnations of this workshop have also led to international collaborative teams, and we anticipate future benefits of a similar nature.