The Problem of Tori in Phase Space

Abstract

A fundamental premise of Hamiltonian chaos is the existence and properties of tori in phase space. More than a geometrical construct, these structures underlie the very dynamics of both classical and quantal systems. Although presented in many introductory textbooks on nonlinear dynamics, the structure of tori in phase space is rarely as transparent as is often presented. Here we outline some of the mathematics of the tori and illustrate a few of the geometric and topologically idiosyncrasies.