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.

Contents:

  • 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.

Show description

Read or Download The KAM Story:A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov–Arnold–Moser Theory PDF

Similar chaos & systems books

Beyond the Second Law: Entropy Production and Non-equilibrium Systems (Understanding Complex Systems)

The second one legislation, a cornerstone of thermodynamics, governs the common path of dissipative, non-equilibrium techniques. however it says not anything approximately their genuine charges or the chance of fluctuations concerning the regular. This interdisciplinary booklet, written and peer-reviewed via foreign specialists, offers fresh advances within the look for new non-equilibrium rules past the second one legislations, and their functions to a variety of platforms throughout physics, chemistry and biology.

Atlas of Physarum Computing

The slime mold Physarum polycephalum is a huge mobile obvious by way of the unaided eye. It behaves as an clever nonlinear spatially prolonged lively medium encapsulated in an elastic membrane. The phone optimises its development styles in configurations of attractants and repellents. This behaviour is interpreted as computation.

Mathematical Analysis of Complex Cellular Activity (Frontiers in Applied Dynamical Systems: Reviews and Tutorials)

This ebook includes overview articles on mathematical body structure that take care of heavily similar issues yet have been written and will be learn independently. the 1st article studies the fundamental idea of calcium oscillations (common to nearly all mobilephone types), together with spatio-temporal behaviors resembling waves.

Strong Nonlinear Oscillators: Analytical Solutions (Mathematical Engineering)

This textbook provides the movement of natural nonlinear oscillatory platforms and numerous answer methods which provide the approximate ideas of the robust nonlinear oscillator equations. It provides the author’s original method for the analytical resolution method of the natural nonlinear oscillator approach.

Additional info for The KAM Story:A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov–Arnold–Moser Theory

Sample text

Download PDF sample

Rated 4.96 of 5 – based on 47 votes