| List of colour plates | p. ix |
| Preface | p. xiii |
| Acknowledgements | p. xv |
| How to read the book | p. xvi |
| The phenomenon: complex motion, unusual geometry | p. 1 |
| Chaotic motion | p. 3 |
| What is chaos? | p. 3 |
| Examples of chaotic motion | p. 4 |
| Phase space | p. 19 |
| Definition of chaos; a summary | p. 21 |
| How should chaotic motion be examined? | p. 22 |
| Brief history of chaos | p. 23 |
| Fractal objects | p. 24 |
| What is a fractal? | p. 24 |
| Types of fractals | p. 32 |
| Fractal distributions | p. 40 |
| Fractals and chaos | p. 45 |
| Brief history of fractals | p. 47 |
| Introductory concepts | p. 49 |
| Regular motion | p. 51 |
| Instability and stability | p. 51 |
| Instability, randomness and chaos | p. 59 |
| Stability analysis | p. 65 |
| Emergence of instability | p. 67 |
| How to determine manifolds numerically | p. 73 |
| Stationary periodic motion: the limit cycle (skiing on a slope) | p. 76 |
| General phase space | p. 79 |
| Driven motion | p. 90 |
| General properties | p. 90 |
| Harmonically driven motion around a stable state | p. 95 |
| Harmonically driven motion around an unstable state | p. 98 |
| Kicked harmonic oscillator | p. 100 |
| Fixed points and their stability in two-dimensional maps | p. 103 |
| The area contraction rate | p. 105 |
| General properties of maps related to differential equations | p. 106 |
| The world of non-invertible maps | p. 108 |
| In what systems can we expect chaotic behaviour? | p. 109 |
| Investigation of chaotic motion | p. 111 |
| Chaos in dissipative systems | p. 113 |
| Baker map | p. 114 |
| Kicked oscillators | p. 131 |
| Henon-type maps | p. 147 |
| Parameter dependence: the period-doubling cascade | p. 149 |
| General properties of chaotic motion | p. 154 |
| The trap of the 'butterfly effect' | p. 159 |
| Determinism and chaos | p. 168 |
| Summary of the properties of dissipative chaos | p. 171 |
| What use is numerical simulation? | p. 172 |
| Ball bouncing on a vibrating plate | p. 174 |
| Continuous-time systems | p. 175 |
| The water-wheel | p. 181 |
| The Lorenz model | p. 187 |
| Transient chaos in dissipative systems | p. 191 |
| The open baker map | p. 193 |
| Kicked oscillators | p. 199 |
| How do we determine the saddle and its manifolds? | p. 201 |
| General properties of chaotic transients | p. 202 |
| Summary of the properties of transient chaos | p. 210 |
| Significance of the unstable manifold | p. 211 |
| The horseshoe map | p. 213 |
| Parameter dependence: crisis | p. 214 |
| Transient chaos in water-wheel dynamics | p. 217 |
| Other types of crises, periodic windows | p. 219 |
| Fractal basin boundaries | p. 221 |
| Other aspects of chaotic transients | p. 225 |
| Chaos in conservative systems | p. 227 |
| Phase space of conservative systems | p. 227 |
| The area preserving baker map | p. 230 |
| The origin of the baker map | p. 233 |
| Kicked rotator - the standard map | p. 234 |
| Connection between maps and differential equations | p. 236 |
| Chaotic diffusion | p. 239 |
| Autonomous conservative systems | p. 242 |
| General properties of conservative chaos | p. 250 |
| Summary of the properties of conservative chaos | p. 259 |
| Homogeneously chaotic systems | p. 260 |
| Ergodicity and mixing | p. 261 |
| Conservative chaos and irreversibility | p. 262 |
| Chaotic scattering | p. 264 |
| The scattering function | p. 265 |
| Scattering on discs | p. 266 |
| Scattering in other systems | p. 274 |
| Chemical reactions as chaotic scattering | p. 276 |
| Summary of the properties of chaotic scattering | p. 277 |
| Applications of chaos | p. 279 |
| Spacecraft and planets: the three-body problem | p. 279 |
| Chaos in the Solar System | p. 284 |
| Rotating rigid bodies: the spinning top | p. 285 |
| Chaos in engineering practice | p. 292 |
| Climate variability and climatic change: Lorenz's model of global atmospheric circulation | p. 293 |
| Chaos in different sciences | p. 300 |
| Controlling chaos | p. 303 |
| Vortices, advection and pollution: chaos in fluid flows | p. 304 |
| Environmental significance of chaotic advection | p. 315 |
| Epilogue: outlook | p. 318 |
| Turbulence and spatio-temporal chaos | p. 320 |
| Appendix | p. 322 |
| Deriving stroboscopic maps | p. 322 |
| Writing equations in dimensionless forms | p. 325 |
| Numerical solution of ordinary differential equations | p. 329 |
| Sample programs | p. 332 |
| Numerical determination of chaos parameters | p. 337 |
| Solutions to the problems | p. 342 |
| Bibliography | p. 370 |
| Index | p. 387 |
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