Conference on "Global Dynamics Beyond Uniform Hyperbolicity"

“超越统一双曲性的全球动力学”会议

• 批准号: 1314157
• 负责人: Keith Burns
• 金额: $ 4.94万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-03-15 至 2014-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1314157&HistoricalAwards=false
• 关键词: Conference; Global; Dynamics; Beyond; Uniform

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.

该提案要求为美国参与者提供资金参加“超越统一双曲性的全球动力学”会议，该会议将于 2013 年 5 月 27 日至 6 月 7 日在波兰贝德勒沃巴纳赫中心举行。本次会议是一系列国际会议中的第六次会议自 2001 年起举办，其中两次在美国举办，主要由 NSF 资助。会议将重点关注可微分动力系统的全局定性研究（拓扑和遍历），特别是非一致双曲的微分同胚和矢量场。涵盖的主要主题包括：-超越双曲性：部分双曲性、非均匀双曲性、奇异双曲性、李雅普诺夫指数、维数、统计属性。-全局和半局部属性：C1 拓扑、分叉。-其他主题：区间动力学、叶状结构。这项对平滑动力系统的研究起源于建立太阳系稳定性的早期努力。 亨利·庞加莱（Henri Poincare）和乔治·伯克霍夫（George Birkhoff）等早期先驱发现了稳定性和不稳定的机制，从而启动了双曲动力系统的研究。大约在同一时间，几何学家艾伯哈德·霍普夫 (Eberhard Hopf) 使用双曲方法来研究负弯曲空间（例如以闵可夫斯基空间为模型的空间）中的测地线（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，成为动力学的基石之一。 该会议是每隔几年举行一次的系列会议之一，汇聚了代表五大洲的真正国际专家组，探讨双曲线之外的最新发展。 通过这些研讨会接触到这项前沿工作，刺激了上一代美国研究生的研究进步，其中许多人将在本次研讨会上发言。 该研讨会的前几届也催生了国际合作团队，我们预计未来也会带来类似性质的好处。