Bifurcations address responses of systems when parameters change. In experiments, that parameter may be a knob we turn up or down.
Applications range from patterns in catalysis, embryogenesis, animal gaits, or fluid dynamics, to hysteresis, instabilities of high speed trains, catastrophic climate change, and symmetry breaking in cosmology. Mathematically, failure of the implicit function theorem is a key feature. We will learn about topics and techniques like dimension reduction, elementary catastrophes, Euler's rod, group invariance and equivariance, Hopf bifurcation, subharmonic oscillations, time reversibility, and transitions to homoclinic chaos.
Prerequisite: some introductory course in differential equations, or equivalent courage. The course will adapt to your background, and
fill in gaps when necessary. From semester 5.
For references see the books of [Alligood, Sauer, Yorke],[V.I. Arnold],[Broer, Takens], [Chow, Hale], [Kielhofer], [Yuri Kuznetsov], [Guckenheimer,Holmes], [Marsden, McCracken], [L.P. Shilnikov, A.L. Shilinikov,Turaev], [Vanderbauwhede], and [Wainwright]. But do not read all of that!
Outlook: seminars, bachelor theses, master's theses, and PhD thesis work using Dynamical Systems methods.