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TitleErgodic Theory, Analysis, and Efficient Simulation of Dynamical Systems [electronic resource] / edited by Bernold Fiedler
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001
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Descript XI, 820 p. online resource


This book summarizes and highlights progress in our understanding of Dyยญ 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


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 โ{128}{148} 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 Selbergโ{128}{153}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

Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering mathematics Probabilities Statistical physics Dynamical systems Mathematics Applications of Mathematics Analysis Statistical Physics Dynamical Systems and Complexity Probability Theory and Stochastic Processes


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