Wednesday 13 Feb 2019: Mathematics Colloquium: Periods and chaos in dynamical systems
Prof. Michael Benedicks - Uppsala University, Sweden
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.