Math 716, Ordinary Differential Equations

spring 2020

Instructor Sigurd Angenent, Van Vleck hall 609.
Prerequisites A thorough understanding of undergraduate real analysis (e.g. as in chapters 1—9 of Rudin’s Principles of Mathematical Analysis.)
Topics
  1. Existence and uniqueness theorems for diffeqs in $\R^n$
  2. Stable, unstable, and center manifolds of fixed points; bifurcation theory point of view.
  3. Topological dynamics (flows, invariant sets, recurrence)
  4. Poincaré—Bendixon theorem
  5. Chaotic dynamics (Poincaré’s homoclinic tangle and Smale's horseshoe in various concrete examples).
Homework There will be short homework assignments every other week.
Exams There will be one midterm exam, and one final exam. Both will be take home exams.
Textbook We will very loosely follow the book by Luis Barreira and Claudia Valls, Ordinary Differential Equations (Qualitative Theory), 1st edition, AMS Graduate Studies in Mathematics, volume 137. Book website