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Chaotic Dynamics An Introduction Based on Classical Mechanics

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ISBN-10: 0521547830

ISBN-13: 9780521547833

Edition: 2005

Authors: Tamas Tel, Marton Gruiz, Szilard Hadobas, Katalin Kulacsy

List price: $89.99
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Description:

It has been discovered over the past few decades that even motions in simple systems can have complex and surprising properties. This volume provides a clear introduction to these chaotic phenomena, based on geometrical interpretations and simple arguments, without the need for prior in-depth scientific and mathematical knowledge. Richly illustrated throughout, its examples are taken from classical mechanics whose elementary laws are familiar to the reader. In order to emphasize the general features of chaos, the most important relations are also given in simple mathematical forms, independent of any mechanical interpretation.
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Book details

List price: $89.99
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 8/24/2006
Binding: Paperback
Pages: 428
Size: 6.75" wide x 9.75" long x 0.75" tall
Weight: 1.892
Language: English

List of colour plates
Preface
Acknowledgements
How to read the book
The phenomenon: complex motion, unusual geometry
Chaotic motion
What is chaos?
Examples of chaotic motion
Phase space
Definition of chaos; a summary
How should chaotic motion be examined?
Brief history of chaos
Fractal objects
What is a fractal?
Types of fractals
Fractal distributions
Fractals and chaos
Brief history of fractals
Introductory concepts
Regular motion
Instability and stability
Instability, randomness and chaos
Stability analysis
Emergence of instability
How to determine manifolds numerically
Stationary periodic motion: the limit cycle (skiing on a slope)
General phase space
Driven motion
General properties
Harmonically driven motion around a stable state
Harmonically driven motion around an unstable state
Kicked harmonic oscillator
Fixed points and their stability in two-dimensional maps
The area contraction rate
General properties of maps related to differential equations
The world of non-invertible maps
In what systems can we expect chaotic behaviour?
Investigation of chaotic motion
Chaos in dissipative systems
Baker map
Kicked oscillators
Henon-type maps
Parameter dependence: the period-doubling cascade
General properties of chaotic motion
The trap of the 'butterfly effect'
Determinism and chaos
Summary of the properties of dissipative chaos
What use is numerical simulation?
Ball bouncing on a vibrating plate
Continuous-time systems
The water-wheel
The Lorenz model
Transient chaos in dissipative systems
The open baker map
Kicked oscillators
How do we determine the saddle and its manifolds?
General properties of chaotic transients
Summary of the properties of transient chaos
Significance of the unstable manifold
The horseshoe map
Parameter dependence: crisis
Transient chaos in water-wheel dynamics
Other types of crises, periodic windows
Fractal basin boundaries
Other aspects of chaotic transients
Chaos in conservative systems
Phase space of conservative systems
The area preserving baker map
The origin of the baker map
Kicked rotator - the standard map
Connection between maps and differential equations
Chaotic diffusion
Autonomous conservative systems
General properties of conservative chaos
Summary of the properties of conservative chaos
Homogeneously chaotic systems
Ergodicity and mixing
Conservative chaos and irreversibility
Chaotic scattering
The scattering function
Scattering on discs
Scattering in other systems
Chemical reactions as chaotic scattering
Summary of the properties of chaotic scattering
Applications of chaos
Spacecraft and planets: the three-body problem
Chaos in the Solar System
Rotating rigid bodies: the spinning top
Chaos in engineering practice
Climate variability and climatic change: Lorenz's model of global atmospheric circulation
Chaos in different sciences
Controlling chaos
Vortices, advection and pollution: chaos in fluid flows
Environmental significance of chaotic advection
Epilogue: outlook
Turbulence and spatio-temporal chaos
Appendix
Deriving stroboscopic maps
Writing equations in dimensionless forms
Numerical solution of ordinary differential equations
Sample programs
Numerical determination of chaos parameters
Solutions to the problems
Bibliography
Index