Manifolds on the Verge of a Regularity Breakdown

Series: 
Research Horizons Seminar
Wednesday, October 30, 2013 - 12:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
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School of Mathematics
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In dynamical systems, the long term behavior is organized by invariant manifolds that serve as landmarks that organize the traffic. There are two main theorems (established around 40-60 years ago) that tell you that these manifolds persist under small perturbations: KAM theorem and the theory of normally hyperbolic manifolds. In recent times there have been constructive proofs of these results which also lead to effective algorithms which allow to explore what happens in the border of the applicability of the theorems. We plan to review the basic concepts and present the experimental results.