Mathematical Sciences: NSF/CBMS Regional Conference in the Mathematical Sciences - Number Theory and Dynamical Systems;June 1-5, 1992

我们知道，丢番图近似中的某些问题与力学中的一些问题是有联系的。例如，在小行星带中，具有木星轨道的某些合理周期的小行星轨道是缺失的，而其他的是存在的。这种联系既发生在哈密顿系统中，也发生在耗散系统中的“锁模”现象中。在过去的几年里，使用重整化方案来研究各种通往混沌的路线，这些联系变得更加精确。在数论方面，最近构造了具有精确自相似性质的“算术分形”。此外，可以使用动力系统研究一维和多维的丢番图近似。该项目将支持于1992年6月1-5日在加州州立大学弗雷斯诺分校举行的NSF-CBMS数论和动力系统数学科学区域研究会议。美国贝尔实验室的Jeffrey Lagarias博士将担任首席讲师。为了激发人们对数学研究的兴趣和活动，美国国家科学基金会每年都支持一些NSF-CBMS数学科学区域研究会议。每个为期五天的会议都有一位杰出的讲师，他就一个重要的当前研究主题在数学科学的一个重点领域发表十次演讲。讲师随后根据这些讲座准备一篇说明性的专著，通常由美国数学学会或工业与应用数学学会出版，或由美国统计协会和数理统计研究所联合出版。这些会议的某些特点区别于典型的研究会议。这些是：(1)由一位领先的实践者专注于一个重要和及时的研究领域；(2)通过区域重点来持续影响和局部刺激；(3)对质量、广度和及时性进行小组审查；(4)为更广泛的受众出版专著。

It is known that there are connections between certain problems in diophantine approximation and problems in mechanics. For example, asteroid orbits having certain rational periods of the orbit of Jupiter are missing in the asteroid belt, while others are present. Such connections occur both in Hamiltonian systems and in "mode-locking" phenomena in dissipative systems. In the last few years these connections have been made more precise using renormalization schemes for studying various routes to chaos. On the number theory side, "arithmetic fractals" with exact self-similarity properties have recently been constructed. In addition, diophantine approximations in both one and several dimensions can be studied using dynamical systems. This project will support an NSF-CBMS Regional Research Conference in the Mathematical Sciences on Number Theory and Dynamical Systems to be held June 1-5, 1992 at California State University, Fresno. Dr. Jeffrey Lagarias of AT&T Bell Laboratories will be the principal lecturer. To stimulate interest and activity in mathematical research, the National Science Foundation each year supports a number of NSF-CBMS Regional Research Conferences in the Mathematical Sciences. Each five-day conference features a distinguished lecturer who delivers ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences. The lecturer subsequently prepares an expository monograph based upon these lectures, which is normally published by the American Mathematical Society or the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Certain features differentiate these conferences from typical research conferences. These are: (1) Focus on a single important and timely area of research by a leading practitioner, (2) Continued effect and local stimulation through regional emphasis, (3) Panel review for quality, breadth, and timeliness, and (4) Published monographs for a wider audience.