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Dynamical Systems with Homoclinic Tangles

Mathematical Physics & Probability

Speaker: Pieter Collins, UC Berkeley
Location: 693 Kerr
Start time: Tue, Nov 16 1999, 4:10PM

Homoclinic and heteroclinic tangles are among the most common and important features of dynamical systems. Most approaches to studying these tangles, such as Smale's proof of the existence of horseshoes has been based upon local analytic estimates. I'll go over some of these results, and then talk about an approach to studying surface diffeomorphisms (and 3D flows etc) by using global topological information (Nielsen fixed-point theory). I'll show how to use these methods to find symbolic dynamics for the Henon map and Duffing's equation.