Tutorial: Introduction to bifurcation theory, part 2

In this second part of our introduction to bifurcation theory, we look at the method called normal forms. That method aims at simplifying the nonlinear terms of a differential equation as much as possible, leaving only so-called resonant terms. Bifurcations of these simplified equations can be studied more easily. We discuss two examples: the Hopf, or Poincaré-Andronov-Hopf bifurcation, and the Bogdanov-Takens bifurcation near a point with a double zero eigenvalue. Intro: 0:00 Recap of part 1: 0:13 Normal forms: 8:18 Homological equation: 15:41 1D bifurcations: 25:34 Hopf bifurcation: 35:04 Double zero eigenvalue: 56:49 Bogdanov-Takens bifurcation: 1:05:46 Related lecture notes: https://arxiv.org/abs/math.HO/0111177 (chapter 3) https://arxiv.org/abs/math.HO/0111178 (chapter 2) Other tutorials:    • Tutorials   #bifurcation #dynamical_system #normal_form