Series: Mathematics Colloquium

Date: Thursday, October 23, 2003

Time: 4:30 - 5:30 PM

Place: 101 Osmond Building (note unusual location)

Hosts: Bryna Kra, Yakov Pesin

Refreshments: 3:45 - 4:30 PM, in 212 McAllister

Speaker: James Yorke, University of Maryland

Title: Pure Chaos, a New Class of Maps in the Plane: The Movie

Abstract:  

Examples have played a key role in understanding dynamical
systems. Plykin for example found a superb well-known example of a map
in the plane that has a chaotic attractor on which the dynamics is
uniformly hyperbolic, and in particular is uniformly stretching. The
Plykin example has been difficult to understand, and we show how it
can easily be understood through video animations. The animations lead
us to a new class of maps that are uniformly hyperbolic, smooth, and
area preserving (on the invariant set). They have the nice properties
of the piecewise linear "Baker map" but our maps have no
discontinuities. We use computer animations throughout as an aid to
visualization. This is joint work with graduate student J. T. Halbert.