Nonlinear Dynamics at the Free University Berlin

Winter 2019/2020

BMS-Course
Bifurcations: Theory and Applications

Prof. Dr. Bernold Fiedler

Recitation sessions: Alejandro López Nieto


Schedule, Wintersemester 2019/2020

Lecture:
Tuesday and Thursday 10-12:00, A3/SR 130
Tutorials:
Alejandro López, Thursday 8:30-10:00 (Sharp!) A7/SR 140

Pass Criteria

Solve correctly at least 25% of the assignments. Hand in solution attempts for at least 50% of the assignments.
Present a correct solution to an assignment on the blackboard in the recitation session at least once.
Pass the written exam.

Course description

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.


References

For references see the books of [Alligood, Sauer, Yorke], [V.I. Arnold], [Broer, Takens], [Chow, Hale], [Kielhöfer], [Yuri Kuznetsov], [Guckenheimer, Holmes], [Marsden, McCracken], [L.P. Shilnikov, A.L. Shilinikov, Turaev], [Vanderbauwhede], and [Wainwright]. But do not read all of that!

Slides from the talk at TU Berlin 21.10.19 (Slides)

Outlook: seminars, bachelor theses, master's theses, and PhD thesis work using Dynamical Systems methods.

Homework assignments

Please form teams of two and hand in your joint solutions.

  1. Assignment, due October 29, 12:00 (PDF)
  2. Assignment, due November 6, 12:00 (PDF)
  3. Assignment, due November 13, 12:00 (PDF)
  4. Assignment, due November 20, 12:00 (PDF)

  1. Extra Assignment, due November 13, 12:00 (PDF)
switch Last change: Nov. 12, 2019
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