KAM theory demystified

May 30, 2014

Many popular accounts describe chaos theory as something that emerged as ever-more-powerful computers were used to model physical systems in such disparate fields as climatology, financial markets, fluid flow, or epidemiology, to name just a few. If Kolmogorov-Arnold-Moser (or KAM) theory is mentioned in these accounts, it is usually to say that it is very important, but too mathematical or difficult to be discussed in detail. This is partly understandable, but also unfortunate, since KAM theory is a central part of the story. Explaining KAM theory and putting it in context shows that it not only lies at the heart of chaos theory, but that it is essential to modern science. KAM theory unravels conundrums in classical mechanics that go back to Henri Poincare and Isaac Newton, shows that the orbits of certain planetary systems may be eternally stable under ideal conditions, and raises questions about the foundations of statistical mechanics that have yet to be fully answered. The development of KAM theory is also full of human drama, involving leading researchers from Russia and Western Europe as well as others from around the globe.

The new book "The KAM Story: A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory" by Professor H Scott Dumas discusses this and more in a readable style aimed primarily at mathematically literate scientists, but also accessible to those with less mathematical training (a large glossary is provided for the reader's convenience). Anyone with an interest in modern mathematical physics and its ramifications deserves to know the story told in this book.
More information about the present book can be found at http://www.worldscientific.com/worldscibooks/10.1142/8955.

World Scientific

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