## Chaotic dynamics of nonlinear systemsCovering all essential topics, this book introduces the major paradigms in the transition to chaos as exhibited by dynamic systems -- all in a coherent and logically integrated format. Every route to chaos in clearly illustrated with examples of how it progresses in specific dynamical systems such as the logistical map, the Lorenz system, and more. Focusing mostly on dissipative systems, this book examines both concepts of mappings and differential dynamics. Includes a chapter on fractal dimension and two chapters on the experimental measurements of chaos. |

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### Contents

Introduction | 1 |

OneDimensional Maps | 13 |

Universality Theory | 33 |

Copyright | |

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### Common terms and phrases

2-cycle approximation area-preserving Arnold attracting set binary center manifold chaotic dynamics chapter coefficients computation consider constant coordinates corresponding curves cycle elements damped pendulum defined denote differential equations digits discussed disk dynamo dynamical system eigenvalues eigenvectors example Feigenbaum FIGURE finite fixed point flip bifurcation flow fractal dimension frequency given gives Henon map Hopf bifurcation initial conditions initial point integrable intermittency invariant manifolds iterations laminar phase LCEs limit cycle linear logistic map Lorenz system Lyapunov dimension Lyapunov exponent LZ complexity map parameter measure motion nonlinear normal form obtain one-dimensional maps period-doubling periodic orbit perturbation phase space plane plot Poincare section refer renormalization rescaling resonance result scaling self-similar sequence shows simple pendulum sketch solution stable strange attractor string supercycle surface tangent tent map theorem trajectory transformation transistion to chaos trapping region twist map two-dimensional maps universal function unstable unstable manifold values variables vector field zero