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.
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.
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