Topological Dynamics in Real and Complex Systems

University Of Alabama At Birmingham, Birmingham AL

Investigators

Abstract

The proposal deals with several topics in low-dimensional dynamics. The PI plans to investigate the topological dynamics of laminations; in particular he would like to further develop the dynamics of growing trees and use it to study the behavior of the vertices of the Julia set. He also wants to consider classes of non-analytic plane maps for whom analogs of well-known results for polynomials can be proven. Other directions of his research are related to attractos for classes of rational maps and to further developing the rotation theory which studies coexistence of cycles depending on their characteristics similar to rotation numbers for circle maps of degree one. The theory of dynamical systems gives tools to study complex systems, for example the evolution of a complicated deterministic process over time. There is a rich and distinguished tradition of using these powerful tools in other sciences like communication theory, statistical physics, and chemical kinetics.