Braided Solutions of Differential Equations

Friday, February 14, 2014 - 10:15am - 11:05am
Keller 3-180
Jan Bouwe Van den Berg (Vrije Universiteit)
Pieces of string or curves in three dimensional space may be knotted or
braided. This topological tool can be used to study certain types of nonlinear
differential equations. In particular, such an approach leads to forcing
theorems in the spirit of the famous period three implies chaos for interval
maps. We have identified three types of differential equations that respect the braid structure, and for these we can construct Morse-Conley-Floer type (homological) invariants. I will also illustrate how the topological arguments can be combined with a computer-assisted approach.
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