Ergodic theory, analysis, and efficient simulation of dynamical systems
This 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
Aufsatzsammlung
xi, 820 pages : illustrations (some color) ; 25 cm
9783540412908, 3540412905
46538515
Random Attractors: Robustness, Numerics and Chaotic Dynamics / Gunter Ochs
Self-Similar Measures / Christoph Bandt
Continuation of Low-Dimensional Invariant Subspaces in Dynamical Systems of Large Dimension / Wolf-Jurgen Beyn, Winfried Kless and Vera Thummler
On Hybrid Methods for Bifuraction and Center Manifolds for General Operators / Klaus Bohmer
Dimension Theory of Smooth Dynamical Systems / Jorg Schmeling
Collision of Control Sets / Fritz Colonius and Wolfgang Kliemann
The Algorithms Behind GAIO-Set Oriented Numerical Methods for Dynamical Systems / Michael Dellnitz, Gary Froyland and Oliver Junge
Polynomial Skew Products / Manfred Denker and Stefan-M. Heinemann
Transfer Operator Approach to Conformational Dynamics in Biomolecular System / Ch. Schutte, W. Huisinga and P. Deuflhard
Simulation and Numerical Analysis of Dendritic Growth / Michael Fried and Andreas Veeser
Bifurcation Phenomena and Dynamo Effect in Electrically Conducting Fluids / F. Feudel, S. Rudiger and N. Seehafer
Cascades of Homoclinic Doubling Bifurcations / Ale Jan Homburg
Existence, Bifurcation, and Stability of Profiles for Classical and Non-Classical Shock Waves / Heinrich Freistuhler, Christian Fries and Christian Rohde
Dynamical Systems of Population Dynamics / K.P. Hadeler and Johannes Muller
Topological and Measurable Dynamics of Lorenz Maps / Gerhard Keller and Matthias St. Pierre
Three-Dimensional Steady Capillary-Gravity Waves / Mariana Haragus-Courcelle and Klaus Kirchgassner
Discretization, Inflation and Perturbation of Attractors / L. Grune and P.E. Kloeden
Aspects on Data Analysis and Visualization for Complicated Dynamical Systems / J. Becker, D. Burkle and R.-T. Happe / [and others]
Non-Smooth Dynamical Systems: An Overview / Markus Kunze and Tassilo Kupper
Forced Symmetry Breaking and Relative Periodic Orbits / Frederic Guyard and Reiner Lauterbach
On Dynamics and Bifurcations of Nonlinear Evolution Equations Under Numerical Discretization / Christian Lubich
Evolution of Microstructure: an Example / Felix Otto
An Extension of the Thermodynamic Formalism Approach to Selberg's Zeta Function for General Modular Groups / Cheng-Hung Chang and Dieter Mayer
Stability and Diffusive Dynamics on Extended Domains / Alexander Mielke, Guido Schneider and Hannes Uecker
Dimension Estimates for Invariant Sets of Dynamical Systems / Volker Reitmann
On the Inverse Problem of Fractal Compression / Hannes Hartenstein, Matthias Ruhl and Dietmar Saupe / [and others]
The Orbit Space Method: Theory and Application / Matthias Rumberger and Jurgen Scheurle
Multi-Pulse Homoclinic Loops in Systems with a Smooth First Integral / Dmitry Turaev
Quantum Chaos and Quantum Ergodicity / A. Backer and F. Steiner
Periodic Orbits and Attractors for Autonomous Reaction-Diffusion Systems / Matthias Buger
Unconditionally Stable Explicit Schemes for the Approximation of Conservation Laws / Christiane Helzel and Gerald Warnecke