# Mathematics Colloquia and Seminars

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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.