Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

1. Front Matter

   Pages I-XI

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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

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.

• algorithms
• analysis
• calculus
• chaos
• dimension
• dynamical systems
• efficient simulation
• ergodic theory
• invariant measures
• large time behaviour
• quantum chaos

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

  Bernold Fiedler

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