Hamiltonian Chaos
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.
Cite
@article{arxiv.2604.12976,
title = {Hamiltonian Chaos},
author = {Steven Tomsovic},
journal= {arXiv preprint arXiv:2604.12976},
year = {2026}
}
Comments
Chapter for the Quantum Chaos volume in 'Comprehensive Quantum Mechanics', to be published by Elsevier (Main editor: R. B. Mann; volume editors: S. Gnutzmann and K. \.Zyczkowski),