Youtor
Tutorial Introduction to bifurcation theory part 2
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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
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