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Applied Mathematics Seminar
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John Guckenheimer
Department of Mathematics, Cornell University

The Birth of Chaos

Wednesday 3rd March 14:05-14:55pm, Carslaw 173.

The term chaos was first applied to dynamical systems by Li and Yorke in 1975, but the phenomenon 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.