Dynamics is the study of systems which evolve with known rules. We want to understand whether the long term behavior is predictable or chaotic. For example, is the solar system stable? Very often, this amounts to studying recursively defined sequences. After presenting various dynamical systems and showing what chaos is, I will focus on sequences of the form

Ζn+1 = Ζ2n + c with Ζ ∈ C and c ∈ C.

For such sequences, the locus of chaos is known as a Julia set. I will present a result (joint with Arnaud Cheritat) that there exist parameters c ∈ C for which chaos prevails: with positive probability, a randomly chosen initial point Ζ0 will have unpredictable behavior.

This is a joint colloquium co-sponsored ICERM and the Clay Mathematics Institute. Thursday, May 3, 2012 from 4:00pm-5:00pm. There will be a reception immediately following the talk.

Image for "Special Colloquium:
Xavier Buff, Université Paul Sabatier,
Clay Mathematics Institute Senior Scholar