Includes bibliographical references and index

Random Attractors: Robustness, Numerics and Chaotic Dynamics / Ochs, Gunter -- Self-Similar Measures / Bandt, Christoph -- Continuation of Low-Dimensional Invariant Subspaces in Dynamical Systems of Large Dimension / Beyn, Wolf-Jürgen (and others.) -- On Hybrid Methods for Bifurcation and Center Manifolds for General Operators / Böhmer, Klaus -- Dimension Theory of Smooth Dynamical Systems / Schmeling, Jörg -- Collision of Control Sets / Colonius, Fritz (and others) -- The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems / Dellnitz, Michael (and others) -- Polynomial Skew Products / Denker, Manfred (and others.) -- Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems / Schütte, Ch. (and others) -- Simulation and Numerical Analysis of Dendritic Growth / Fried, Michael (and others) -- Bifurcation Phenomena and Dynamo Effect in Electrically Conducting Fluids / Feudel, F. (and others) -- Cascades of Homoclinic Doubling Bifurcations / Homburg, Ale Jan -- Existence, Bifurcation, and Stability of Profiles for Classical and Non-Classical Shock Waves / Freistühler, Heinrich (and others) Dynamical Systems of Population Dynamics / Hadeler, K. P. (and others) -- Topological and Measurable Dynamics of Lorenz Maps / Keller, Gerhard (and others) -- Three-Dimensional Steady Capillary-Gravity Waves / Hărăguş-Courcelle, Mariana (and others) -- Discretization, Inflation and Perturbation of Attractors / Grüne, L. (and others) -- Aspects on Data Analysis and Visualization for Complicated Dynamical Systems / Becker, J. (and others) -- Non-Smooth Dynamical Systems: An Overview / Kunze, Markus (and others) -- Forced Symmetry Breaking and Relative Periodic Orbits / Guyard, Frédéric (and others) -- On Dynamics and Bifurcations of Nonlinear Evolution Equations Under Numerical Discretization / Lubich, Christian -- Evolution of Microstructure: an Example / Otto, Felix -- An Extension of the Thermodynamic Formalism Approach to Selberg’s Zeta Function for General Modular Groups / Chang, Cheng-Hung (and others) -- Stability and Diffusive Dynamics on Extended Domains / Mielke, Alexander (and others) -- Dimension Estimates for Invariant Sets of Dynamical Systems / Reitmann, Volker

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.