Geography of Order and Chaos in Mechanics

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

  • Bruno Cordani

Part of the Progress in Mathematical Physics book series (PMP, volume 64)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Bruno Cordani
    Pages 1-16
  3. Bruno Cordani
    Pages 83-130
  4. Bruno Cordani
    Pages 131-146
  5. Bruno Cordani
    Pages 175-209
  6. Bruno Cordani
    Pages 211-227
  7. Bruno Cordani
    Pages 229-264
  8. Bruno Cordani
    Pages 265-304
  9. Bruno Cordani
    Pages 305-308
  10. Back Matter
    Pages 309-332

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 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, but mostly will be an exceptional reference for Ph.D. students with an interest in perturbation theory.


KAM theory MATLAB programs Nekhoroshev theorem normal forms numerical integration perturbation theory

Authors and affiliations

  • Bruno Cordani
    • 1
  1. 1., Dipartimento di MatematicaUniversità degli StudiSoresina (CR)Italy

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