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Kam Story, The: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-arnold-moser Theory
This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science.The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory).Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.
Hamiltonian Dynamical Systems
From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.
Hamiltonian Systems with Three or More Degrees of Freedom
A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also r...
Averaging Methods in Nonlinear Dynamical Systems
Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.
Essays on Classical and Quantum Dynamics
A collection of essays suitable for college students or practitioners of theoretical physics, written for a symposium, "Fundamental problems in classical and quantum mechanics," in Washington, DC, October 1988. Among the classical topics are fractal time stochastics in the glass transition, Kovalevski exponents, and chaos in spin-wave systems. Quantum dynamics is discussed from such perspectives as topology and quantization, a simple normal-form approach to anharmonic oscillators, and channeling radiation of electrons in crystal lattices. In addition, one of the 13 essays discusses nonlinear dynamics in brain processes. Annotation copyrighted by Book News, Inc., Portland, OR
The KAM Story
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Beam Halo Dynamics, Diagnostics, and Collimation
This book documents comprehensive reviews and state-of-the-art studies in the dynamics, diagnostics, and collimation of charged-particle beam halo and in beam-beam interaction. Challenges and solutions to major accelerator facilities in Europe, Asia, and America in the domain of high intensity, high energy, and high brightness charged particles are presented. Latest breakthroughs in physical analysis, engineering design, and experimental tests are included.
The Son of Porthos
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