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Geography of Order and Chaos in Mechanics

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Produktnummer: 18598a0b68372b472c9774fe534cf8a61a
Autor: Cordani, Bruno
Themengebiete: KAM theorem Kepler problem Nekhoroshev theorem perturbation theory quasi-integrable Hamiltonian system solar system stability
Veröffentlichungsdatum: 05.09.2024
EAN: 9783031722257
Auflage: 2
Sprache: Englisch
Seitenzahl: 395
Produktart: Gebunden
Verlag: Springer International Publishing
Untertitel: Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools
Produktinformationen "Geography of Order and Chaos in Mechanics"
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.Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novel ways, but perhaps its most useful feature is its inclusion of software to reproduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computer programming to visualize and experiment with the distribution of order, chaos and resonances in various Hamiltonian systems.This monograph will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, as well as an exceptional reference for PhD students with an interest in perturbation theory.The Second Edition includes a new chapter on theoretical and numerical results in the study of the solar system's (in)stability obtained since publication of the First Edition, clarifying the topological mechanism that causes the sudden increase in Mercury's eccentricity. An updated version of the companion software is also provided, which contains new features and better Graphical User Interfaces. Thanks to the compiled versions, all the software can be used even if the user does not have access to a MATLAB installation.
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