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Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

  • Conference proceedings
  • © 2001

Overview

Editors:
  1. Bernold Fiedler

    1. Freie Universität Berlin Institut für Mathematik I, Berlin, Germany

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  • Presentation of very recent results in a major research area
  • Includes supplementary material: sn.pub/extras

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Table of contents (31 papers)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Random Attractors: Robustness, Numerics and Chaotic Dynamics

    • Gunter Ochs
    Pages 1-30

  3. Self-Similar Measures

    • Christoph Bandt
    Pages 31-46

  4. Continuation of Low-Dimensional Invariant Subspaces in Dynamical Systems of Large Dimension

    • Wolf-Jürgen Beyn, Winfried Kleß, Vera Thümmler
    Pages 47-72

  5. On Hybrid Methods for Bifurcation and Center Manifolds for General Operators

    • Klaus Böhmer
    Pages 73-107

  6. Dimension Theory of Smooth Dynamical Systems

    • Jörg Schmeling
    Pages 109-129

  7. Collision of Control Sets

    • Fritz Colonius, Wolfgang Kliemann
    Pages 131-144

  8. The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems

    • Michael Dellnitz, Gary Froyland, Oliver Junge
    Pages 145-174

  9. Polynomial Skew Products

    • Manfred Denker, Stefan-M. Heinemann
    Pages 175-189

  10. Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems

    • Ch. Schütte, W. Huisinga, P. Deuflhard
    Pages 191-223

  11. Simulation and Numerical Analysis of Dendritic Growth

    • Michael Fried, Andreas Veeser
    Pages 225-252

  12. Bifurcation Phenomena and Dynamo Effect in Electrically Conducting Fluids

    • F. Feudel, S. Rüdiger, N. Seehafer
    Pages 253-270

  13. Cascades of Homoclinic Doubling Bifurcations

    • Ale Jan Homburg
    Pages 271-286

  14. Existence, Bifurcation, and Stability of Profiles for Classical and Non-Classical Shock Waves

    • Heinrich Freistühler, Christian Fries, Christian Rohde
    Pages 287-309

  15. Dynamical Systems of Population Dynamics

    • K. P. Hadeler, Johannes Müller
    Pages 311-332

  16. Topological and Measurable Dynamics of Lorenz Maps

    • Gerhard Keller, Matthias St. Pierre
    Pages 333-361

  17. Three-Dimensional Steady Capillary-Gravity Waves

    • Mariana Hărăguş-Courcelle, Klaus Kirchgässner
    Pages 363-397

  18. Discretization, Inflation and Perturbation of Attractors

    • L. Grüne, P. E. Kloeden
    Pages 399-416

  19. Aspects on Data Analysis and Visualization for Complicated Dynamical Systems

    • J. Becker, D. Bürkle, R.-T. Happe, T. Preußer, M. Rumpf, M. Spielberg et al.
    Pages 417-430

  20. Non-Smooth Dynamical Systems: An Overview

    • Markus Kunze, Tassilo Küpper
    Pages 431-452
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Keywords

About this book

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.

Editors and Affiliations

  • Freie Universität Berlin Institut für Mathematik I, Berlin, Germany

    Bernold Fiedler

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