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