By H Scott Dumas
This is a semi-popular arithmetic publication aimed toward a extensive 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 publication must also attract much less mathematically proficient readers with an curiosity within the heritage or philosophy of science.
The scope of the publication is extensive: it not just describes KAM idea in a few aspect, but in addition offers its historic context (thus displaying why it used to be a “breakthrough”). additionally mentioned are functions of KAM idea (especially to celestial mechanics and statistical mechanics) and the elements of arithmetic and physics during which KAM conception is living (dynamical structures, classical mechanics, and Hamiltonian perturbation theory).
Although a few assets on KAM conception are actually on hand for specialists, this e-book makes an attempt to fill a long-standing hole at a extra descriptive point. It sticks out very essentially from current guides on KAM thought since it leads the reader via an available account of the speculation and areas it in its right context in arithmetic, physics, and the background of science.
- Minimum Mathematical Background
- Leading as much as KAM: A caricature of the History
- KAM Theory
- KAM in Context: Questions, results, Significance
- Other ends up in Hamiltonian Perturbation thought (HPT)
- Physical Applications
- Kolmogorov's 1954 Paper
- Overview of Low-Dimensional Small Divisor Problems
- East Meets West — Russians, Europeans, Americans
- Guide to additional Reading
- Selected Quotations
Readership: Undergraduates, graduates, and researchers commonly attracted to Hamiltonian perturbation idea, statistical mechanics, ergodic conception, Nekhoroshev concept, Arnold diffusion, nonlinear dynamics, dynamical structures, chaos idea, classical mechanics, and the historical past of those subjects.
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The KAM Story:A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov–Arnold–Moser Theory by H Scott Dumas