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Bifurcation and Chaos: Analysis, Algorithms, Applications

  • R. Seydel
  • F. W. Schneider
  • T. Küpper
  • H. Troger

Table of contents

  1. Front Matter
    Pages I-X
  2. J. Amrehn, Th.-M. Kruel, F. W. Schneider, F. Buchholtz
    Pages 19-25
  3. J. Boissonade, V. Castets, E. Dulos, P. De Kepper
    Pages 67-77
  4. Domokos Gábor
    Pages 99-103
  5. M. Eiswirth, A. Freund, J. Ross
    Pages 105-109
  6. M. S. El Naschie, T. Kapitaniak
    Pages 111-115
  7. J. Falzarano, A. Steindl, A. Troesch, H. Troger
    Pages 117-121
  8. E. Gamero, E. Freire, E. Ponce
    Pages 123-127
  9. T. J. Garratt, G. Moore, A. Spence
    Pages 129-133
  10. Johan F. Kaashoek, Herman K. van Dijk
    Pages 177-181
  11. M. Kirby, D. Armbruster, W. Güttinger
    Pages 183-187
  12. U. Kirchgraber, F. Lasagni, K. Nipp, D. Stoffer
    Pages 189-197
  13. W. Kleczka, E. Kreuzer, C. Wilmers
    Pages 199-203
  14. K. Krischer, M. Lübke, W. Wolf, M. Eiswirth, G. Ertl
    Pages 211-215
  15. C.-H. Lamarque, J.-M. Malasoma
    Pages 249-255
  16. R. Luce, J. P. Kernévez
    Pages 257-261
  17. Mario Markus, Carsten Schäfer
    Pages 263-275
  18. U. Parlitz, C. Scheffczyk, T. Kurz, W. Lauterborn
    Pages 283-287
  19. E. J. Ponce-Núñez, E. Gamero
    Pages 295-299
  20. A. J. Rodríguez-Luis, E. Freire, E. Ponce
    Pages 301-306
  21. C. Scheffczyk, U. Parlitz, T. Kurz, W. Lauterborn
    Pages 319-323
  22. H. Sevcikova, M. Marek
    Pages 325-331
  23. Peter Stelter, Walter Sextro
    Pages 343-347

About this book

Introduction

This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. The theme of the conference was Bifurcation and Chaos: Analysis, Algorithms, Ap­ plications. More than 100 scientists from 21 countries presented 80 contributions. Many of the results of the conference are described in the 49 refereed papers that follow. The conference was sponsored by the Deutsche Forschungsgemeinschaft, and by the Deutscher Akademischer Austauschdienst. We gratefully acknowledge the support from these agen­ cies. The science of nonlinear phenomena is evolving rapidly. Over the last 10 years, the emphasis has been gradually shifting. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79). Concerning the range of phenomena, chaos has joined the bifurcation scenarios. As expected, the acceptance of chaos is less emotional among professionals, than it has been in some popular publications. A nalytical methods appear to have reached a state in which basic results of singularities, symmetry groups, or normal forms are everyday experience rather than exciting news. Similarly, numerical algorithms for frequent situations are now well established. Implemented in several packages, such algorithms have become standard means for attacking nonlinear problems. The sophisti­ cation that analytical and numerical methods have reached supports the vigorous trend to more and more applications. Pioneering equations as those named after Duffing, Van der Pol, or Lorenz, are no longer exclusively the state of art.

Keywords

Eigenvalue Laplace operator Volume bifurcation derivative differential equation distribution dynamical systems manifold maximum minimum numerical method ordinary differential equation partial differential equation stability

Editors and affiliations

  • R. Seydel
    • 1
  • F. W. Schneider
    • 2
  • T. Küpper
    • 3
  • H. Troger
    • 4
  1. 1.Abteilung für NumerikUniversität UlmUlmGermany
  2. 2.Institut für Physikalische ChemieUniversität WürzburgWürzburgGermany
  3. 3.Mathematisches InstitutUniversität KölnKölnGermany
  4. 4.Institut für MechanikTechnische Universität WienWienAustria

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