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.

该提案要求为美国的参与者提供资金参加2013年5月27日至2013年5月27日在波兰贝德尔沃的Banach中心举行的“全球动态超越统一双曲线”的会议。该会议是自2001年以来举行的一系列国际会议中的第六次会议，其中两次在美国举行，并在美国举行了两项，并主要由NSF资助。该会议将重点介绍可区分动力学系统的全球定性研究（拓扑和千古化），尤其是差异和矢量领域，这些系统并非均匀双曲线。要涵盖的主要主题之一是： - 贝隆多的超润滑性：部分双重性，非均匀的双重性，奇异的夸张性，Lyapunov指数，维度，统计特性，统计特性，全体属性的特性：C1-访问学，C1-cotogy，c1 tosology，bifurcolcations。太阳系。 亨利·庞卡雷（Henri Poincare）和乔治·伯克霍夫（George Birkhoff）等早期开拓者发现了稳定性和不稳定的机甲主义，从而启动了双波利动力学系统的研究。大约在同一时间，地域埃伯哈德·霍夫夫（Eberhard Hopf）使用双曲线方法来研究负弯曲空间（例如在Minkowski空间上建模的）中地球学（直线）的长期行为。一个世纪后，对双曲动力学系统的研究已成熟的领域，这是动态的基石之一。 这次会议每隔几年举行一次系列赛，汇集了一个真正的国际专家团体，代表5大洲，以探索超出双曲线的最新发展。 通过这些研讨会，通过这些研讨会接触这种尖端的工作，刺激了上一代美国研究生的研究进展，其中许多人将在本研讨会上讲话。 该研讨会的先前化身也导致了国际合作团队，我们预计类似性质的未来收益。