## Ergodic Theory, Analysis, and Efficient Simulation of Dynamical SystemsThis book summarizes and highlights progress in our understanding of Dy namical Systems during six years of the German Priority Research Program "Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems" . The program was funded by the Deutsche Forschungsgemeinschaft (DFG) and aimed at combining, focussing, and enhancing research efforts of active groups in the field by cooperation on a federal level. The surveys in the book are addressed to experts and non-experts in the mathematical community alike. In addition they intend to convey the significance of the results for applications far into the neighboring disciplines of Science. Three fundamental topics in Dynamical Systems are at the core of our research effort: behavior for large time dimension measure, and chaos Each of these topics is, of course, a highly complex problem area in itself and does not fit naturally into the deplorably traditional confines of any of the disciplines of ergodic theory, analysis, or numerical analysis alone. The necessity of mathematical cooperation between these three disciplines is quite obvious when facing the formidahle task of establishing a bidirectional transfer which bridges the gap between deep, detailed theoretical insight and relevant, specific applications. Both analysis and numerical analysis playa key role when it comes to huilding that bridge. Some steps of our joint bridging efforts are collected in this volume. Neither our approach nor the presentations in this volume are monolithic. |

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### Contents

6 | |

31 | |

47 | |

73 | |

Jörg Schmeling | 109 |

Fritz Colonius and Wolfgang Kliemann 131 | 130 |

Michael Dellnitz Gary Froyland and Oliver Junge | 145 |

Manfred Denker and StefanM Heinemann | 175 |

J Becker D Bürkle R T Happe T Preußer M Rumpf | 417 |

Markus Kunze and Tassilo Kiipper | 431 |

Frédéric Guyard and Reimer Lauterbach | 453 |

Christian Lubich | 469 |

Felin Otto | 501 |

ChengHung Chang and Dieter Mayer | 523 |

Alexander Mielke Guido Schneider and Hannes Uecker | 563 |

Volker Reitmann 585 | 584 |

Ch Schütte W Huisinga and P Deufthard | 191 |

Michael Fried and Andreas Veeser 225 | 224 |

F Feudel S Rüdiger and N Seehafer | 253 |

Ale Jan Homburg | 271 |

Heinrich Freistühler Christian Fries and Christian Rohde | 287 |

K P Hadeler and Johannes Müller | 311 |

Gerhard Keller and Matthias St Pierre | 333 |

Mariana HărăgușCourcelle and Klaus Kirchgāssner 363 | 370 |

Grüne and P E Kloeden | 399 |

Hannes Hartenstein Matthias Ruhl Dietmar Saupe | 617 |

Matthias Rumberger and Jürgen Scheurle 649 | 648 |

Dmitry Turaev | 691 |

A Bäcker and F Steiner | 717 |

Matthias Büger 753 | 752 |

Christiane Helzel and Gerald Warnecke | 775 |

Color Plates 805 | 804 |

Author Index | 819 |

### Other editions - View all

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems Collectif Limited preview - 2001 |

Ergodic Theory, Analysis and Efficient Simulation of Dynamical Systems Bernold Fiedler No preview available - 2011 |

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems Bernold Fiedler No preview available - 2013 |

### Common terms and phrases

algorithm analysis applied approximation assume asymptotic behavior bifurcation billiard bounded boxes center manifold computed conservation laws consider constant continuous control set convergence corresponding defined denote density differential equations diffusion dimension discrete domain eigenvalues eigenvector entropy ergodic Ergodic Theory error exists finite fixed point flow fractal code geodesic geodesic flow given global attractor Hausdorff Hausdorff dimension Hence heteroclinic Hilbert homoclinic orbit hyperbolic intersection invariant manifolds invariant measure invariant set Julia set Lemma linear Lorenz map Lyapunov exponents Markov Math Mathematics matrix method multifractal nonlinear numerical obtained orbit space parameter periodic orbit perturbation planar Poincaré Poincaré map polynomial problem proof properties pullback attractor random compact set random dynamical system respect Riemann satisfies scheme sequence smooth spectral stability stochastic subgroup subset surface symmetry tangent Theorem theory tion topological trajectory transfer operator transverse unstable manifold vector field zero zeta function