WHAT CAN COMPLEX TIME TELL US ABOUT REAL TIME DYNAMICS?

Abstract

In this tutorial we will review the successes and limitations of singularity analysis of dynamical systems, the progress made to date and the prospects for future research. By singularity analysis we mean the identification of the nature of all movable (i.e., initial condition dependent) singularities of a dynamical system in the complex time plane, and the study of the (generally complex) solutions of the system, in the vicinity of these singularities. The emphasis will be on the main ideas, methods and techniques, and the presentation will focus on examples and applications. However, a description of the most important theoretical developments and an outline of the main rigorous results will also be given. Our central theme throughout this review will be the connection between complex time singularities and the properties of the solutions of a dynamical system in real time.