Mathematics Colloquium

Mechanisms for chaos

Speaker: Amie Wilkinson, University of Chicago

Location: Warren Weaver Hall 1302

Date: Monday, December 9, 2019, 3:45 p.m.


The term "chaos" refers to highly unpredictable behavior in a closed, deterministic system, butthere is no agreed-upon mathematical definition of a chaotic dynamical system.  Certainly we have a feel for what chaos means: a typical orbit fills the phase space, a small error in initial condition can have disastrous consequences in the long run, and orbits behave in some sense randomly.  
In this talk, I will discuss families of dynamical systems that are typically chaotic and the mechanisms behind this chaotic behavior.
mechanism for a dynamical behavior has three interrelated features:
  •  it is based on rough, geometric features of the system and as little a priori information about the actual dynamics as possible;
  •  it is verifiable in specific examples; and
  •  it is  robust, persistent under perturbations of the system.
While touching upon topics of current research, the talk will be aimed at a graduate student level.