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

众所周知，丢番图逼近中的某些问题与力学中的问题之间存在着联系。例如，小行星带中没有具有木星轨道一定合理周期的小行星轨道，而其他小行星轨道却存在。这种联系既存在于哈密顿系统中，也存在于耗散系统的“锁模”现象中。在过去的几年里，使用重整化方案研究了通向混沌的各种途径，使这些联系变得更加精确。在数论方面，最近已经构造出具有精确自相似性质的“算术分形图”。此外，一维和多维的丢番图逼近都可以用动力系统来研究。该项目将支持将于1992年6月1日至5日在弗雷斯诺加利福尼亚州立大学举行的NSF-CBMS数论和动力系统数学科学区域研究会议。美国电话电报公司贝尔实验室的杰弗里·拉加里亚斯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力，美国国家科学基金会每年都会支持一些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发表十次演讲，该主题是数学科学中一个尖锐的重点领域。讲师随后根据这些讲座编写一份说明性专著，通常由美国数学学会或工业和应用数学学会出版，或由美国统计协会和数学统计研究所联合出版。这些会议的某些特点使其有别于典型的研究会议。它们是：(1)由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)小组审查质量、广度和及时性，以及(4)出版面向更广泛受众的专著。

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.