This book presents the fundamentals of chaos theory in conservative systems and provides a systematic study of the theory of transitional states of physical systems that lie between deterministic and chaotic behavior. The authors begin with the general concepts of Hamiltonian dynamics, stabililty, and chaos, and then discuss the theory of stochastic layers and webs and the numerous applications of this theory, particularly to pattern symmetry. Throughout, they are meticulous in providing a detailed presentation of the material, which enables the reader to learn the necessary computational methods and to apply them to other problems. The inclusion of computer graphics will aid understanding and the final section of the book contains a collection of patterns in art and living nature that will fascinate.
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Book Description
Editorial Reviews
Review
"The serious student of chaos will find this book well worth reading. As a technical review, it is presently unparalleled, and as a provocative introduction to the mysteries of patterns, it is unique." Ronald F. Fox, American Journal of Physics
"...will be of most interest to specialists looking for a source for this material outside the original literature - the only other place much of it can be found." C. Eugene Wayne, Physics Today
"The material in this book can, and should, be incorporated into a senior undergraduate, or first year graduate, mechanics course. This is also an interesting and very readable book for physicists and applied mathematicians who are interested in chaos, irreversibility, and theories of spatial patterns and symmetries. I recommend this book highly...." K.K. Lee, Physics in Canada
"a stimulating book that can provide new ideas on the generation and occurrence of patterns is a wide range of situations." Peter J. Bryant, SIAM Review
"...will be of most interest to specialists looking for a source for this material outside the original literature - the only other place much of it can be found." C. Eugene Wayne, Physics Today
"The material in this book can, and should, be incorporated into a senior undergraduate, or first year graduate, mechanics course. This is also an interesting and very readable book for physicists and applied mathematicians who are interested in chaos, irreversibility, and theories of spatial patterns and symmetries. I recommend this book highly...." K.K. Lee, Physics in Canada
"a stimulating book that can provide new ideas on the generation and occurrence of patterns is a wide range of situations." Peter J. Bryant, SIAM Review
Language Notes
Text: English (translation)
Original Language: Russian
Original Language: Russian
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First Sentence:
The equations of motion in classical physics differ considerably depending upon the subject they describe: a particle, an electromagnetic field, or a fluid. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
separatrix network, stochasticity region, stochastic web, stochastic layer, periodic web, stochastic sea, weak chaos, nonlinear pendulum, plane tilings, separatrix loops, nonlinear resonance, invariant tori, elliptic points, phase portrait, standard mapping, hyperbolic points, invariant curves, stream lines, unperturbed motion, magnetic surfaces, invariant torus, phase plane, stochastic motion, stream function, local isomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Van Hove, Macmillan Magazines Ltd, Maurits Escher, Von Karman New!
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The equations of motion in classical physics differ considerably depending upon the subject they describe: a particle, an electromagnetic field, or a fluid. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
separatrix network, stochasticity region, stochastic web, stochastic layer, periodic web, stochastic sea, weak chaos, nonlinear pendulum, plane tilings, separatrix loops, nonlinear resonance, invariant tori, elliptic points, phase portrait, standard mapping, hyperbolic points, invariant curves, stream lines, unperturbed motion, magnetic surfaces, invariant torus, phase plane, stochastic motion, stream function, local isomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Van Hove, Macmillan Magazines Ltd, Maurits Escher, Von Karman New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 17
books:
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12
books
cite this book:
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- Chaos in Dynamic Systems by G. Zaslavsky on 4 pages
- The Fractal Geometry of Nature by Benoit B. Mandelbrot in Back Matter (1), and Back Matter (2)
- Classical Mechanics by John R. Taylor in Back Matter (1), and Back Matter (2)
- Patterns of Symmetry by Marjorie Senechal in Back Matter (1), and Back Matter (2)
- Tilings and Patterns by Branko Grunbaum in Back Matter (1), and Back Matter (2)
See all 17 books this book cites
- Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers by Robert Hilborn on page 313, and Back Matter
- Quantum Chaos and Quantum Dots (Mesoscopic Physics and Nanotechnology) by Katsuhiro Nakamura in Back Matter
- Chaotic Dynamics and Transport in Classical and Quantum Systems: Proceedings of the NATO Advanced Study Institute on International Summer School on ... II: Mathematics, Physics and Chemistry) by Pierre Collet on page 348
- Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows by Andrew Majda on page 179
- Classical Dynamics: A Contemporary Approach by Jorge V. José in Back Matter
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