Geography of Order and Chaos in Mechanics:
Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools
English | 2024 | ISBN: 3031722256 | 413 Pages | PDF (True) | 33 MB
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.
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