## Analysis and Modelling of Discrete Dynamical SystemsThe theory of dynamical systems, or mappings, plays an important role in various disciplines of modern physics, including celestial mechanics and fluid mechanics. This comprehensive introduction to the general study of mappings has particular emphasis on their applications to the dynamics of the solar system. The book forms a bridge between continuous systems, which are suited to analytical developments and to discrete systems, which are suitable for numerical exploration. Featuring chapters based on lectures delivered at the School on Discrete Dynamical Systems (Aussois, France, February 1996) the book contains three parts - Numerical Tools and Modelling, Analytical Methods, and Examples of Application. It provides a single source of information that, until now, has been available only in widely dispersed journal articles. |

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### Contents

Spectra of Stretching Numbers and Helicity Angles | 55 |

Diffusion and Transient Spectra in a 4Dimensional | 91 |

Distribution of Periodic Orbits in 2D Dynamical Systems | 107 |

Symplectic Integrators | 133 |

Rigorous and Numerical Determination of Rotational | 149 |

Interpolation of Discrete Hamiltonian Systems | 181 |

### Common terms and phrases

2ero analysis analytic approximation Arnold diffusion asteroid Astron asymptotic curves averaged behaviour bifurcations chaotic domain chaotic orbit chaotic region computed consider constant continued fraction Contopoulos coordinates corresponding defined degrees of freedom dimensional diophantine distribution dynamical systems eigenvalues elliptic equation exponentially FIGURE fixed points Fourier frequency map Froeschle function Giorgilli Hamiltonian system helicity angles Henon map homoclinic tangle hyperbolic initial conditions interpolating Hamiltonian intersect invariant curves invariant tori islands of stability KAM theorem linear Lyapunov exponent mapping model method Morbidelli motion Nekhoroshev nonlinear nonresonant normal form number of iterations obtained ordered domains particle periodic orbits perturbing parameter phase space Phys plane Poincare map problem regime regular orbits resonance overlap rotation number Sect shown in Fig si2e solution spectrum standard map stochastic stretching numbers surface of section symplectic integrator symplectic map theorem theory tonian torus trajectory transformation Turchetti values variables variation vector x-axis