How do we Find out What a Dynamical System is Doing?

Thursday, November 20, 1997 - 9:30am - 10:30am
Keller 3-180
James Yorke (University of Maryland)
The Maryland chaos group has developed a number of algorithms aimed at discovering what is happening in a dynamical system of low dimension. In particular I will discuss the BA (Basins and Attractors) routine (developed with Helena Nusse) that aims at finding all the basins and attractors of 2-dimensional maps. It can also find the smallest trapping region that an attractor lies in, with the restriction that the trapping region is a union of grid boxes. Simple reliable algorithms let us find trajectories that lie on the boundary of basins. We call these basin straddle trajectories. Other routines will discussed with some demonstrations using a PC. Mathematicians have saddled the scientific community with the concept of chaotic or strange attractor. Yet except in very rare cases of hyperbolic attractors, it is impossible to conclude for a specific dynamical system rigorously that such an attractor exists. I will discuss alternatives to this theory.