Overview
- Offers a unique approach to the dynamics of quasi-integrable Hamiltonian systems
- Provides a rare opportunity for readers to experiment with and fully conceptualize recent numerical tools via customized MATLAB applications
- Gives a rigorous but clean and uncluttered presentation of perturbaton theory, including clear proofs of the KAM and Nekhoroshev theorems
- Fully describes new, sophisticated techniques for reducing two paradigmatic problems the field to normal forms?
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematical Physics (PMP, volume 64)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Geography of Order and Chaos in Mechanics
Book Subtitle: Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools
Authors: Bruno Cordani
Series Title: Progress in Mathematical Physics
DOI: https://doi.org/10.1007/978-0-8176-8370-2
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, New York 2013
Hardcover ISBN: 978-0-8176-8369-6Published: 17 September 2012
Softcover ISBN: 978-1-4939-0044-2Published: 15 October 2014
eBook ISBN: 978-0-8176-8370-2Published: 29 September 2012
Series ISSN: 1544-9998
Series E-ISSN: 2197-1846
Edition Number: 1
Number of Pages: XVIII, 334
Topics: Mathematical Physics, Differential Geometry, Applications of Nonlinear Dynamics and Chaos Theory, Partial Differential Equations, Numerical and Computational Physics, Simulation, Mathematical Methods in Physics