Local Techniques in Bifurcation Theory and Nonlinear Dynamics

  • G. Iooss
Part of the International Centre for Mechanical Sciences book series (CISM, volume 298)


Let us consider a mass m fastened to two identical springs of constant k and natural length ℓ/cos x 0 .


Normal Form Hopf Bifurcation Taylor Expansion Compatibility Condition Unstable Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    V. Arnold, Chapitres supplémentaires de la théorie des équations différentielles ordinaires. MIR, Moscou, 1980Google Scholar
  2. [2]
    J.M. Gambaudo, Perturbation of a Hopf bifurcation by an external time-periodic forcing. J. Differential Equations. 57, 179–199, 1985MathSciNetGoogle Scholar
  3. [3]
    P. Chossat, G. Iooss, Primary and Secondary Bifurcations in the Couette-Taylor problem. Japan J. Appl. Math. 2, 1, 37–68, 1985MathSciNetMATHGoogle Scholar
  4. [4]
    R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. 1. Interscience Pub. 1953Google Scholar
  5. [5]
    C. Elphick, E. Tirapegui, M. Brachet, P. Coullet, G. Iooss, A simple global characterization for normal forms of singular vector fields. Preprint n° 109 Université de Nice, 1986Google Scholar
  6. [6]
    J. Guckenheimer, P. Holmes, Nonlinear oscillations, Dynamical systems and Bifurcations of vector fields. Applied Maths Sci. 42, Springer, 1983Google Scholar
  7. [7]
    G. Iooss, D.D. Joseph, Elementary stability and Bifurcation theory, U.T.M., Springer-Verlag, 1980Google Scholar
  8. [8]
    T. Kato, Perturbation theory for linear operators. Springer Verlag, 1966.Google Scholar

Copyright information

© Springer-Verlag Wien 1988

Authors and Affiliations

  • G. Iooss
    • 1
  1. 1.Université de NiceNice CedexFrance

Personalised recommendations