## Ergodic Theory, Analysis, and Efficient Simulation of Dynamical SystemsThis book summarizes and highlights progress in Dynamical Systems achieved during six years of the German Priority Research Program "Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems," funded by the Deutsche Forschungsgemeinschaft (DFG). The three fundamental topics of large time behavior, dimension, and measure are tackled with by a rich circle of uncompromisingly rigorous mathematical concepts. The range of applied issues comprises such diverse areas as crystallization and dendrite growth, the dynamo effect, efficient simulation of biomolecules, fluid dynamics and reacting flows, mechanical problems involving friction, population biology, the spread of infectious diseases, and quantum chaos. 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. |

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### Contents

Robustness Numerics and Chaotic Dynamics | 1 |

SelfSimilar Measures | 31 |

Continuation of LowDimensional Invariant Subspaces in Dynamical Systems of Large Dimension | 47 |

On Hybrid Methods for Bifurcation and Center Manifolds for General Operators | 73 |

Dimension Theory of Smooth Dynamical Systems | 109 |

Collision of Control Sets | 131 |

The Algorithms Behind GAIO Set Oriented Numerical Methods for Dynamical Systems | 145 |

Polynomial Skew Products | 175 |

Aspects on Data Analysis and Visualization for Complicated Dynamical Systems | 417 |

An Overview | 431 |

Forced Symmetry Breaking and Relative Periodic Orbits | 453 |

On Dynamics and Bifurcations of Nonlinear Evolution Equations Under Numerical Discretization | 469 |

an Example | 501 |

An Extension of the Thermodynamic Formalism Approach to Selbergs Zeta Function for General Modular Groups | 523 |

Stability and Diffusive Dynamics on Extended Domains | 563 |

Dimension Estimates for Invariant Sets of Dynamical Systems | 585 |

Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems | 191 |

Simulation and Numerical Analysis of Dendritic Growth | 225 |

Bifurcation Phenomena and Dynamo Effect in Electrically Conducting Fluids | 253 |

Cascades of Homoclinic Doubling Bifurcations | 271 |

Existence Bifurcation and Stability of Profiles for Classical and NonClassical Shock Waves | 287 |

Dynamical Systems of Population Dynamics | 311 |

Topological and Measurable Dynamics of Lorenz Maps | 333 |

ThreeDimensional Steady CapillaryGravity Waves | 363 |

Discretization Inflation and Perturbation of Attractors | 399 |

On the Inverse Problem of Fractal Compression | 617 |

Theory and Application | 649 |

MultiPulse Homoclinic Loops in Systems with a Smooth First Integral | 691 |

Quantum Chaos and Quantum Ergodicity | 717 |

Periodic Orbits and Attractors for Autonomous ReactionDiffusion Systems | 753 |

Unconditionally Stable Explicit Schemes for the Approximation of Conservation Laws | 775 |

Color Plates | 805 |

819 | |

### Other editions - View all

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems Bernold Fiedler Limited preview - 2012 |

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 approach approximation assume attractor behavior bifurcation boundary bounded called close coding compact complex computed consider constant construction contains continuous convergence corresponding defined definition denote depends derivative described determined differential equations dimension direction discrete distribution domain dynamical systems eigenvalues error estimates example exists field Figure finite fixed flow fractal function given gives global Hence holds homoclinic hyperbolic implies initial integral invariant linear Lyapunov manifold Markov Math matrix means measure method nonlinear normal Note numerical obtained operator orbit original parameter periodic periodic orbit perturbation phase positive possible probability problem projection proof properties random representation respect satisfies scheme sequence shown smooth solution space stability step structure surface symmetry Theorem theory tion unique unstable values vector waves zero