TL;DR
This paper explores Hamiltonian chaos, its theoretical tools, and its connection to quantum chaos, emphasizing intuitive explanations and the geometry and perturbations of chaotic systems.
Contribution
It provides an overview of Hamiltonian chaos topics, linking classical chaos tools to quantum chaos research and discussing system responses and complexification.
Findings
Illustrates the use of surfaces of section and symbolic dynamics
Explains the geometry and perturbation responses of chaotic systems
Highlights the complexification of Hamiltonian dynamics
Abstract
Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum chaos research problems. The chapter begins with a description of various useful theoretical and computational tools of chaos research, e.g.~surfaces of section, paradigms of chaos, stability analysis, and symbolic dynamics... This is followed by discussions regarding the geometry of chaos, how chaotic systems respond to perturbations, and the complexification of Hamiltonian dynamics. The emphasis is on intuitive explanations and illustrations of various ideas with the references containing more mathematically rigorous expositions.
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