Workshop in Dynamical Systems and Related Topics

摘要该奖项延续了NSF对动力系统及相关主题研讨会2006、2007和2008年秋季会议的部分（但必不可少的）支持。这代表了宾夕法尼亚州立大学半年度动力系统及相关主题研讨会的一半，该研讨会在过去的15年里由宾夕法尼亚州立大学和马里兰州的动力学小组共同主办；马里兰州的比赛每年春天举行。会议基本上涵盖了动力系统的所有主题，在大多数会议中有一个特定的（但不是排他性的）重点领域。在2006年，2007年和2008年，将增加一个几何会议，以解决在动力学和几何之间的边界日益增长的活动。会议的目标是促进数学结果的交流；促进动力系统和相关领域的相互作用和进步；在这些范畴培养社区意识和共同使命感；并为研究生和最近的博士学位获得者的培训以及他们融入动力学社区做出贡献。特别值得一提的是，会议包括了由研究生进行的约8个简短演讲，这些学生获得了一些有趣的新成果。多年来，许多杰出的数学家以及（我们现在看到的）未来的领导者都参加了这次会议。过去节目的历史可以在www.math.psu.edu/research/dynsust/dw.html和www.math.psu.edu/research/dynsust/dw-archive.html上找到。一般来说，动力系统领域研究系统随时间变化的方式，特别是系统的典型轨迹如何随时间变化，以及系统中感兴趣的特性在系统扰动下何时稳定。由于许多数学结构都可以根据它们如何随时间变化来考虑，动力系统使用了广泛的数学学科（包括微分方程、泛函分析、几何、概率论和许多其他学科）。相反，动态方法对其中一些领域的进展作出了重大贡献，但这是在一个深刻而不明显的层面上。最近的一个例子——在数论中！是对格林和陶的工作的动态影响，他们的工作表明素数包含任意长的等差数列。此外，从动力系统的角度对各种实际问题进行了卓有成效的研究，包括目前在天气预报和空间“旅行者”轨道计算中的应用。另一个例子是对“混沌”的研究：对“混沌”进行严格数学描述的现代方法是基于雅所发展的佩辛理论。宾夕法尼亚州立大学动力学和几何中心的成员，以及马里兰州动力学小组成员J. Yorke的开创性工作。

AbstractThis award continues the partial (but essential) support of NSF for the fall meetings of the Workshop in Dynamical Systems and Related Topics for the years 2006, 2007, and 2008. This represents the Penn State half of the Semi-annual Workshop in Dynamical Systems and Related Topics, cosponsored for the last 15 years by the dynamics groups of Penn State and Maryland; the Maryland half is held each spring. The conference covers essentially all topics in dynamical systems, with a particular (but not exclusive) area of emphasis in most meetings. In the years 2006, 2007, and 2008 a Geometry session will be added to address growing activity in the borderline between dynamics and geometry. The goals of the conference are to promote the communication of mathematical results; to facilitate interaction and progress in dynamical systems and related fields; to nurture the sense of community and common mission in these fields; and to contribute to the training of graduate students and recent Ph.D. recipients and to their integration into the dynamics community. In particular, the conference includes special sessions with about 8 short talks by graduate students who received some interesting new results. Over the years the conference has enjoyed the participation of many prominent mathematicians, as well as (we see now) future leaders. A history of past programs can be found at www.math.psu.edu/research/dynsust/dw.html and www.math.psu.edu/research/dynsust/dw-archive.html. In general terms, the field of dynamical systems studies the way in which systems change over time, especially, how typical trajectories of a system behave over time, and when properties of interest in a system are stable under perturbations of the system. Because so many mathematical structures can be considered in terms of how they change over time, dynamical systems uses a broad range of mathematical disciplines (including differential equations, functional analysis, geometry, probability theory and many others). Conversely, the dynamical approach has contributed significantly to progress in some of these fields, at a deep and nonobvious level. A recent example -- in number theory! is the dynamical influence on the work of Green and Tao which showed that the prime numbers contain arbitrarily long arithmetic progressions. In addition, various practical problems are fruitfully studied from the viewpoint of dynamical systems, including current applications in weather forecasting and the computation of orbits of space "voyagers". Another example is study of "chaos": modern methods of rigorous mathematical description of "chaos" are based on Pesin's Theory developed by Ya. Pesin, a member of the Penn State Center for Dynamics and Geometry and on pioneering works of J. Yorke, a member of the Maryland dynamics group.