What is the graph of a dynamical system?
From maps to diffusive partial differential equations
Jim Yorke
Joint work with Roberto De Leo and Chirag Adwani
What is the graph of a dynamical system?
From maps to diffusive partial differential equations
Jim Yorke
Joint work with Roberto De Leo and Chirag Adwani
Abstract
Frequently we describe a dynamical system in terms of its attractors, but that can leave out important information about unstable invariant sets.
A directed graph of a dynamical system is a picture that outlines how the various invariant sets of a dynamical system are related. The simplest example is of the logistic map. Its graph can be extremely complicated. There are dynamical systems with infinitely many attractors, and we want to know how these are dynamically related.