Applied Maths Seminar: Guckenheimer -- The Birth of Chaos

John Guckenheimer, 
Department of Mathematics, Cornell University 

The term chaos was first applied to dynamical systems by Li and Yorke in 1975, but the
pheomenon was discovered in "dissipative" dynamical systems much earlier by Cartwright
and Littlewood.  They studied a system, the forced van der Pol equation, that was
formulated and studied by van der Pol in the 1920’s as a model of electronic circuits
instrumental in the development of radio.  The details of their work are very
complicated and they appeared more than a decade after they announced the main results.
This lecture will recount this history.  It will then present recent studies of the
forced van der Pol equation that both simplify and extend the results of Cartwright and
Littlewood.  The highlight of this recent work is the thesis of Radu Haiduc that proves
that there are parameter regions of the forced van der Pol equation for which the system
is structural stable and chaotic.  The setting for this recent work is geometric
singular perturbation theory that analyzes generic properties of dynamical systems with
multiple time scales.  

http://www.maths.usyd.edu.au/u/AppliedSeminar/abstracts/2010/guckenheimer.html


Note: This year’s seminar location is Carslaw 173!