By H Scott Dumas

This is a semi-popular arithmetic ebook geared toward a wide readership of mathematically literate scientists, specifically mathematicians and physicists who're no longer specialists in classical mechanics or KAM conception, and scientific-minded readers. components of the booklet also needs to entice much less mathematically proficient readers with an curiosity within the heritage or philosophy of science.

The scope of the booklet is large: it not just describes KAM conception in a few aspect, but additionally offers its ancient context (thus exhibiting why it was once a “breakthrough”). additionally mentioned are purposes of KAM conception (especially to celestial mechanics and statistical mechanics) and the elements of arithmetic and physics within which KAM conception is living (dynamical platforms, classical mechanics, and Hamiltonian perturbation theory).

Although a couple of resources on KAM thought at the moment are to be had for specialists, this publication makes an attempt to fill a long-standing hole at a extra descriptive point. It stands proud very sincerely from current courses on KAM conception since it leads the reader via an available account of the idea and locations it in its right context in arithmetic, physics, and the heritage of science.


  • Introduction
  • Minimum Mathematical Background
  • Leading as much as KAM: A caricature of the History
  • KAM Theory
  • KAM in Context: Questions, outcomes, Significance
  • Other leads to Hamiltonian Perturbation concept (HPT)
  • Physical Applications
  • Appendices:
    • Kolmogorov's 1954 Paper
    • Overview of Low-Dimensional Small Divisor Problems
    • East Meets West — Russians, Europeans, Americans
    • Guide to extra Reading
    • Selected Quotations
    • Glossary

Readership: Undergraduates, graduates, and researchers largely drawn to Hamiltonian perturbation thought, statistical mechanics, ergodic conception, Nekhoroshev conception, Arnold diffusion, nonlinear dynamics, dynamical platforms, chaos concept, classical mechanics, and the historical past of those subjects.

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