Transport in Two-Dimensional Maps: General Principles and Results

In Chapter 1 we introduced a variety of applications for which some of the questions relevant to the applications could be phrased in terms of a phase space transport problem. These phase space transport problems were motivated by considering systems that could be expressed as perturbations of integrable one-degree-of-freedom Hamiltonian systems. This was instructive because the unperturbed systems possessed qualitatively different motions, bounded by separatrices, that could be easily characterized in the context of the application. When the system was perturbed, it was natural to discuss transitions between these regions of qualitatively different motions.