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.
