International Workshop on Global Dynamics beyond Uniform Hyperbolicity

本提案描述了将于2006年5月在芝加哥举行的关于部分夸张及其相关主题的国际会议。会议的目标是传播最近在该领域取得的突破，并促进在过去10年中对该领域采取的不同方法的整合和协作。这将是一系列会议中的第三次，该会议始于2001年5月由PIS组织的一次由NSF支持的会议。偏双曲主题出现在70年代初，并已成为复杂(“混沌”)动力系统理论发展的一个中心方向。对部分双曲性及其相关系统的研究已经大大超出了双曲动力学的经典背景，这是因为人们意识到，动力系统对实验现象的许多实际应用确实需要更广泛的理论。这一提议的广泛影响和学术价值是多方面的，也是相互关联的：*由于会议的重点是微型课程、研究生和最近的博士。美国的S将接触到该领域的尖端研究，甚至在这些知识通过其他方式传播之前。*本次会议全体会议的一部分将专门讨论部分双曲系统理论在机械系统以及生物学中某些系统中的最新应用。*这次会议将把来自四大洲的与会者聚集在一起；预计会议将在这些与会者和美国与会者之间产生新的合作项目。*最后，会议将提高美国研究人员在部分双曲及相关动力系统领域的全球知名度。

AbstractThis proposal describes an international conference on partial hyperpbolicity and related topics to be held in Chicago in May, 2006. The goals of the conference are to disseminate recent breakthroughs in the field and to promote integration of and collaboration among the different approaches to the area that have developed in the past 10 years. This will be the third conference in a series that began with an NSF-supported conference organized by the PIs in May, 2001.The topic of partial hyperbolicity emerged in the early seventies and has become a central direction in which the theory of complicated ("chaotic") dynamical systems has developed. The study of partial hyperbolicity and related systems has extended significantly beyond the classical setting of hyperbolic dynamics, driven by the realization that many practical applications of dynamical systems to experimental phenomena do require a much broader theory. The broader impact and intellectual merits of this proposal are multifold and interrelated: * Because of the conference focus on minicourses, graduate students and recent Ph.D.'s within the US will be exposed to cutting edge research in the area, even before this knowledge has been disseminated by other means. *A portion of the plenary talks in this conference will be devoted to recent applications of the theory of partially hyperbolic systems to mechanical systems, as well as certain systems in biology. *The conference will bring together participants from four continents; the expectation is that the conference will lead to new collaborative ventures between these participants and US participants. *Finally, the conference will increase the worldwide visibility of US researchers in the area of partially hyperbolic and related dynamical systems.