Geography of Order and Chaos in Mechanics: Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools

This monograph explores the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems – such as the hydrogen atom and the solar system, with the associated Arnold web – through modern tools such as the frequency-modified Fourier transform, wavelets, and the frequency-modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems.