Dynamical Systems

Dynamical system and representation theory

In this talk, a practical method is described for computing the classical normal form of vector fields near the bifurcation point. Some necessary formulas are derived and applied to the anharmonic oscillator, the Bogdanov-Takens bifurcation, the 3D nilpotent problem, and elastic pipe conveying fluid,  to demonstrate the applicability of the theoretical results.
 Then, a review will be given of the developments in the last decade concerning the classification of unique normal forms in 3D nilpotent problems.