Normal Forms and Bifurcation of Plane Vector Fields
From Sunday, 15. September 2002
To Friday, 30. May 2003
Hits : 11
Teachers:
Chengzhi Li (Peking University)

Programa:
  1. Introduction
  2. Center Manifolds
    • Existence, uniqueness and smoothness of global center manifolds
    • Local center manifolds
  3. Normal forms
    • Normal forms for differential equations near a critical point
    • Poincaré’s theorem and Siegel’s theorem
    • Examples
    • Some new developments on normal forms
  4. Bifurcation of Plane Vector Fields
    • Bifurcation and its codimension
    • Bifurcation of equilibria : codimension one and higher
    • Homoclinic bifurcation : codimension one and higher
    • Heteroclinic bifurcation
    • Multiple limit cycle bifurcation
    • Poincar´e bifurcation : Abelian integrals and limit cycles
    • Bogdanov-Takens bifurcation : codimension two and higher
    • Some examples


References:
  1. S.-N. Chow, C. Li and D.Wang, "Normal Forms and Bifurcation of Plane Vector Fields", Cambridge University Press, 1994.
  2. J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields", Springer-Verlag, New York, 1983.
  3. V. I. Arnold, "Geometric Methods in the Theory of Ordinary Differential Equations", Springer-Verlag, New York, 1983.
Location Universitat Autònoma de Barcelona