Dynamics on Two-Dimensional Surfaces

Northwestern University, Evanston IL

Investigators

Abstract

This is a proposal to investigate aspects of low dimensional dynamical systems. The most important long term project is to better understand a topological description of C^r generic area preserving diffeomorphisms of surfaces where r > 1. In addition the proposer hopes to investigate the action of more general groups than the integers or the reals on surfaces, and in particular area preserving actions. Professor Franks will continue his investigation of the dynamics of surface maps. The study of such transformations, especially area preserving ones, has a long history going back to Poincare and G. D. Birkhoff. There are numerous applications of results in this area to classical mechanics as well as more modern chaotic dynamics. The proposed research will address questions concerning the existence of periodic behavior in area preserving two-dimensional discrete dynamical systems and a topological description of the dynamics of such systems.