13 - Physics of chaotic systems

Summary

Introduction

Depending on one’s point of view, the realization that solutions to even simple deterministic dynamical systems could produce highly irregular – chaotic – behavior happened 40 years ago with the publication of Edward Lorenz’ seminal paper “Deterministic nonperiodic flow” or probably more than 100 years ago with Poincaré’s study of complicated orbits in three-body problems of classical Hamiltonian mechanics. Each study indicated the prevalence of complex orbits in classical state space when only a few degrees of freedom were involved. Each study was an unpleasant surprise to physical scientists, and Poincaré’s work was roundly ignored for more than half a century, while Lorenz’ results were reported in a geosciences journal read by a relatively small group of atmospheric scientists.

Each result, one on the celestial mechanics of Hamiltonian systems and the other on a severe approximation to the dissipative fluid dynamics of convection, had no place in the mainstream pursuits of the day. This was in remarkable contrast to the development of the wave equation for nonrelativistic quantum theory, or the crystal structure of DNA. Both of these were at the core of widely identified important problems and were developments for which a huge body of scientists was prepared. Scientists were not even looking in the right direction when chaotic behavior in deterministic systems was found.