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Bifurcations of Planar Vector Fields

Proceedings of a Meeting held in Luminy, France, Sept. 18–22, 1989

  • Editors
  • Jean-Pierre Françoise
  • Robert Roussarie
Conference proceedings

Part of the Lecture Notes in Mathematics book series (LNM, volume 1455)

Table of contents

  1. Front Matter
    Pages I-VI
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  2. Retard à la bifurcation : du local au global
    Bernard Candelpergher, Francine Diener, Marc Diener
    Pages 1-19
  3. On bifurcation of limit cycles from centers
    Carmen Chicone
    Pages 20-43
  4. On the saddle loop bifurcation
    Freddy Dumortier, Robert Roussarie
    Pages 44-73
  5. Finitude des cycles-limites et accelero-sommation de l’application de retour
    J. Ecalle
    Pages 74-159
  6. Limit cycles and zeroes of Abelian integrals satisfying third order picard — Fuchs equations
    Ljubomir Gavrilov, Emil Horozov
    Pages 160-186
  7. On the basin of attraction of dissipative planar vector fields
    A. Gasull, J. Sotomayor
    Pages 187-195
  8. Periodic lines of curvature bifurcating from Darbouxian umbilical connections
    C. Gutierrez, J. Sotomayor
    Pages 196-229
  9. Conditions for a centre and the bifurcation of limit cycles in a class of cubic systems
    NG Lloyd, JM Pearson
    Pages 230-242
  10. On first integrals of linear systems, Frobenius integrability theorem and linear representations of Lie algebras
    Jean Moulin Ollagnier, Jean-Marie Strelcyn
    Pages 243-271
  11. Cyclicite finie des polycycles hyperboliques de champs de vecteurs du plan mise sous forme normale
    A. Mourtada
    Pages 272-314
  12. Bifurcation of limit cycles
    L. M. Perko
    Pages 315-333
  13. Universal unfolding of a singularity of a symmetric vector field with 7-jet C∞-equivalent to y ∂/∂x+(±x3 ±x6y) ∂/∂y
    Christiane Rousseau
    Pages 334-355
  14. Bifurcation in a quartic polynomial system arising in biology
    Franz Rothe, Douglas S. Shafer
    Pages 356-368
  15. On the finiteness of certain boundary cycles for NTH degree polynomial vector fields
    Shi Songling
    Pages 369-372
  16. Algebraic integrals of quadratic systems with a weak focus
    Dana Schlomiuk
    Pages 373-384
  17. Rotated vector fields decomposition method and its application
    Ye Yanqian
    Pages 385-392
  18. Remarks on the delay of the loss of stability of systems with changing parameter
    Henryk Żoładek
    Pages 393-396
  19. Back Matter
    Pages 397-398
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About these proceedings

Keywords

Vector field bifurcations dynamical systems ordinary differential equations periodic orbits

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0085387
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-53509-6
  • Online ISBN 978-3-540-46722-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site