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

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.

List of contents

Preface.- List of Figures.- 1 Introductory Survey.- 2 Analytical Mechanics and Integrable Systems.- 3 Perturbation Theory.- 4 Numerical Tools I: ODE Integration.- 5 Numerical Tools II: Detecting Order, Chaos, and Resonances.- 6 The Kepler Problem.- 7 The KEPLER Program.- 8 Some Perturbed Keplerian Systems.- 9 The Multi-Body Gravitational Problem.- Bibliography.- Index.

Summary

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.

Product details

• Authors: Bruno Cordani
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2014
• EAN: 9781493900442
• ISBN: 978-1-4939-0044-2
• No. of pages: 334
• Dimensions: 157 mm x 235 mm x 20 mm
• Weight: 539 g
• Illustrations: XVIII, 334 p.
• Series: Progress in Mathematical Physics; Progress in Mathematical Physics
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; Analysis, B, Physics, Mathematics and Statistics, Theoretical, Mathematical and Computational Physics, Differential Geometry, Mathematical physics, Partial Differential Equations, Nonlinear science, Differential calculus & equations, Numerical and Computational Physics, Simulation, Mathematical Methods in Physics, Differential & Riemannian geometry, Dynamics & statics, Applications of Nonlinear Dynamics and Chaos Theory, Statistical physics, Nonlinear Optics