Wednesday 13 Feb 2019Mathematics Colloquium: Periods and chaos in dynamical systems

Prof. Michael Benedicks - Uppsala University, Sweden

H103 14:30-15:30

In dynamical systems such as ordinary differential equations or iterations of functions one sees in computer experiments two typical behaviours: A trajectory is attracted to a periodic orbit or there is chaotic behavior: two nearby initial points separate exponentially fast and a typical orbit distributes statistically in the phase space. I will try to explain the present understanding of this:
When is the picture of the computer experiments true mathematically?

Are these two phenomena all that can happen?

Can these phenomena exist simultaneously for one system?

I particular I will describe the work by Lennart Carleson and me on chaotic behavior, “strange attractors”, in the classical Henon family, and time permitting, I will describe recent work with Liviana Palmisano on coexisting sinks and chaotic behavior in this family.

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