Geography of Order and Chaos in Mechanics

Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools

Bruno Cordani

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Springer New York img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Theoretische Physik

Beschreibung

This original monograph aims to explore 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—including for example the hydrogen atom or 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.

Geography of Order and Chaos in Mechanics will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, but mostly will be an exceptional reference for Ph.D. students with an interest in perturbation theory.

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Schlagwörter

KAM theory, Nekhoroshev theorem, numerical integration, partial differential equations, normal forms, MATLAB programs, perturbation theory