Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

ISBN-13: 9783642625244 / Angielski / Miękka / 2013 / 820 str.

Bernold Fiedler

Opis

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."

Spis treści

Project Ludwig Arnold and Wolfgang Krieger - Gunther Ochs: Random attractors: robustness, numerics and chaotic dynamics.- Project Christoph Bandt - Christoph Bandt: Self-similar measures.- Project Wolf-Jürgen Beyn - Wolf-Jürgen Beyn, Winfried Kleß, and Vera Thümmler: Continuation of low-dimensional invariant subspaces in dynamical systems of large dimension.- Project Hans-Günter Bothe - Jörg Schmeling: Dimension theory of smooth dynamical systems.- Project Klaus Böhmer - Klaus Böhmer: On hybrid methods for bifurcation and center manifolds for general operators.- Project Fritz Colonius - Fritz Colonius and Wolfgang Kliemann: Collision of control sets.- Project Michael Dellnitz - Michael Dellnitz, Gary Froyland, and Oliver Junge: The algorithms behind GAIO - Set oriented numerical methods for dynamical systems.- Project Manfred Denker - Manfred Denker and Stefan-M. Heinemann: Polynomial skew products.- Project Peter Deuflhard - Ch. Schütte, W. Huisinga, and P. Deuflhard: Transfer operator approach to conformational dynamics in biomolecular systems.- Project Gerhard Dziuk - Michael Fried and Andreas Veeser: Simulation and numerical analysis of dendritic growth.- Project Fred Feudel, Jürgen Kurths, and Norbert Seehafer - F. Feudel, S. Rüdiger, N. Seehafer: Bifurcation phenomena and dynamo effect in electrically conducting fluids.- Project Bernold Fiedler - Ale Jan Homburg: Cascades of homoclinic doubling bifurcations.- Project Heinrich Freistühler and Dietmar Kröner - Heinrich Freistühler, Christian Fries, and Christian Rohde: Existence, bifurcation, and stability of profiles for classical and non-classical shock waves.- Project Karl Peter Hadeler - K.P. Hadeler and Johannes Müller: Dynamical systems of population dynamics.- Project Gerhard Keller - Gerhard Keller and Matthias St.Pierre: Topological and measurable dynamics of Lorenz maps.- Project Klaus Kirchgässner - Mariana Haragus-Courcelle and Klaus Kirchgässner: Three-dimensional steadycapillary-gravity waves.- Project Peter Kloeden - L. Grüne and P.E. Kloeden: Discretization, inflation and perturbation of attractors.- Project Dietmar Kröner and Martin Rumpf - J. Becker, D. Bürkle, R.-T. Happe, T. Preußer, M. Rumpf, M. Spielberg, R. Strzodka: Aspects on data analysis and visualization for complex dynamical systems.- Project Tassilo Küpper and Markus Kunze - Tassilo Küpper and Markus Kunze: Non-smooth dynamical systems: An overview.- Project Reiner Lauterbach - Frédéric Guyard and Reiner Lauterbach: Forced symmetry breaking and relative periodic orbits.- Project Christian Lubich - Christian Lubich: On dynamics and bifurcations of nonlinear evolution equations under numerical discretization.- Project Stephan Luckhaus and Stefan Müller - Felix Otto: Evolution of microstructure: an example.- Project Dieter Mayer - Cheng-Hung Chang and Dieter Mayer: An extension of the thermodynamic formalism approach to Selberg's zeta function for general modular groups.- Project Alexander Mielke and Guido Schneider - Alexander Mielke, Guido Schneider, and Hannes Uecker: Stability and diffusive dynamics on extended domains.- Project Volker Reitmann - Volker Reitmann: Dimension estimates for invariant sets of dynamical systems.- Project Dietmar Saupe - Hannes Hartenstein, Matthias Ruhl, Dietmar Saupe, and Edward R. Vrscay: On the inverse problem of fractal compression.- Project Jürgen Scheurle - Matthias Rumberger and Jürgen Scheurle: The orbit space method: theory and application.- Project Klaus R. Schneider - D.V. Turaev: Multi-pulse homoclinic loops in systems with a smooth first integral.- Project Frank Steiner - A. Bäcker and F. Steiner: Quantum chaos and quantum ergodicity.- Project Hans-Otto Walther - Matthias Büger: Periodic orbits and attractors for autonomous reaction-diffusion systems.- Project Gerald Warnecke - Christiane Helzel and Gerald Warnecke: Unconditionally stable explicit schemes for the approximation of conservation laws