Front cover image for Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

This 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
eBook, English, 2001
Springer Berlin Heidelberg, Berlin, Heidelberg, 2001
1 online resource (XI, 820 pages)
9783642565892, 9783642625244, 3642565891, 364262524X
840292245
Printed edition:
Random Attractors: Robustness, Numerics and Chaotic Dynamics
Self-Similar Measures
Continuation of Low-Dimensional Invariant Subspaces in Dynamical Systems of Large Dimension
On Hybrid Methods for Bifurcation and Center Manifolds for General Operators
Dimension Theory of Smooth Dynamical Systems
Collision of Control Sets
The Algorithms Behind GAIO
Set Oriented Numerical Methods for Dynamical Systems
Polynomial Skew Products
Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems
Simulation and Numerical Analysis of Dendritic Growth
Bifurcation Phenomena and Dynamo Effect in Electrically Conducting Fluids
Cascades of Homoclinic Doubling Bifurcations
Existence, Bifurcation, and Stability of Profiles for Classical and Non-Classical Shock Waves
Dynamical Systems of Population Dynamics
Topological and Measurable Dynamics of Lorenz Maps
Three-Dimensional Steady Capillary-Gravity Waves
Discretization, Inflation and Perturbation of Attractors
Aspects on Data Analysis and Visualization for Complicated Dynamical Systems
Non-Smooth Dynamical Systems: An Overview
Forced Symmetry Breaking and Relative Periodic Orbits
On Dynamics and Bifurcations of Nonlinear Evolution Equations Under Numerical Discretization
Evolution of Microstructure: an Example
An Extension of the Thermodynamic Formalism Approach to Selberg's Zeta Function for General Modular Groups
Stability and Diffusive Dynamics on Extended Domains
Dimension Estimates for Invariant Sets of Dynamical Systems
On the Inverse Problem of Fractal Compression
The Orbit Space Method: Theory and Application
Multi-Pulse Homoclinic Loops in Systems with a Smooth First Integral
Quantum Chaos and Quantum Ergodicity
Periodic Orbits and Attractors for Autonomous Reaction-Diffusion Systems
Unconditionally Stable Explicit Schemes for the Approximation of Conservation Laws
Color Plates
Author Index
English