Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

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Bernold Fiedler
Springer Science & Business Media, Dec 6, 2012 - Mathematics - 820 pages
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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.
 

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Contents

Gunter Ochs
6
Christoph Bandt
31
WolfJürgen Beyn Winfried Kleff and Vera Thiimmler
47
Klaus Böhmer
73
Jörg Schmeling
109
Fritz Colonius and Wolfgang Kliemann 131
130
Michael Dellnitz Gary Froyland and Oliver Junge
145
Manfred Denker and StefanM Heinemann
175
J Becker D Bürkle R T Happe T Preußer M Rumpf
417
Markus Kunze and Tassilo Kiipper
431
Frédéric Guyard and Reimer Lauterbach
453
Christian Lubich
469
Felin Otto
501
ChengHung Chang and Dieter Mayer
523
Alexander Mielke Guido Schneider and Hannes Uecker
563
Volker Reitmann 585
584

Ch Schütte W Huisinga and P Deufthard
191
Michael Fried and Andreas Veeser 225
224
F Feudel S Rüdiger and N Seehafer
253
Ale Jan Homburg
271
Heinrich Freistühler Christian Fries and Christian Rohde
287
K P Hadeler and Johannes Müller
311
Gerhard Keller and Matthias St Pierre
333
Mariana HărăgușCourcelle and Klaus Kirchgāssner 363
370
Grüne and P E Kloeden
399
Hannes Hartenstein Matthias Ruhl Dietmar Saupe
617
Matthias Rumberger and Jürgen Scheurle 649
648
Dmitry Turaev
691
A Bäcker and F Steiner
717
Matthias Büger 753
752
Christiane Helzel and Gerald Warnecke
775
Color Plates 805
804
Author Index
819
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