## Elementary Symbolic Dynamics and Chaos in Dissipative SystemsThis book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical rigour. The author used elementary mathematics and calculus, and relied on physical intuition whenever possible. Substantial attention is paid to numerical techniques in the study of chaos. Part of the book is based on the publications of Chinese researchers, including those of the author's collaborators. |

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### Contents

Preface | 1 |

OneDimensional Mappings | 20 |

Group Equation | 79 |

Elementary Symbolic Dynamics | 101 |

Circle Mappings and TwoDimensional Maps | 205 |

Chaos in Ordinary Differential Equations | 253 |

Characterization of Chaotic Attractors | 337 |

Transient Behaviour | 417 |

457 | |

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### Common terms and phrases

2-cycle admissible words behaviour bifurcation diagram boundaries calculated chaos chaotic attractor chaotic bands chaotic orbits chaotic region circle map convergence corresponding critical points curve defined denote determined eigenvalues entropy example exists Feigenbaum Figure finite fixed point forced Brusselator frequency function Hénon map heteroclinic intersections homoclinic infinite initial point interval invariant inverse iteration letters linear logistic map Lorenz model Lyapunov exponents matrix mode-locking monotonic nonlinear one-dimensional mappings ordinary differential equations oscillator parameter space parameter value parity period-doubling bifurcation period-doubling sequence period-n-tupling sequences periodic orbits periodic points periodic windows phase space phase transitions Phys Poincaré map Poincaré section quasiperiodic regime renormalization group equation RL*R rotation number saddle Schwarzian derivative shown in Fig solution spectra spectrum stable manifolds superstable orbit symbolic dynamics symbolic sequence symmetry tangent bifurcation theorem theory topological trajectory transformation transients unimodal maps unstable periodic vectors zero