Speaker: Evelyn Sander (George Mason University)
Time: 2025-11-10 11:00-12:00
Zoom Meeting ID:844 0594 7424 Passcode:076895
Abstract: Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically each time it hits the boundary. The successive bounce location plus bounce angle forms a two-dimensional iterated map, which was first studied by Birkhoff. On elliptical tables, the dynamics of billiard maps are completely integrable. The Birkhoff conjecture proposes that this is the only smooth convex table for which this is true. In this spirit, we present an implicit real analytic method for billiard maps on perturbed elliptical tables. This method allows us to compute stable and unstable manifolds using the parametrization method. This in turn allows us to establish transverse homoclinic orbits, thereby showing chaos. While the results as yet are numerical only, our method is devised so it can in future be validated. This is joint work with Patrick Bishop, Summer Chenoweth, and Emmanuel Fleurantin at George Mason University and Jay Mireles James at Florida Atlantic University.
About Speaker: Professor Evelyn Sander is a researcher studying both the theory and applications of Dynamical Systems working at George Mason University. In particular, she is an expert on Topological Dynamical Systems, Bifurcation Theory, Computer assisted proofs, and their applications to Science and Engineering. In addition to these, she is a current council member of SIAM, and served as the Editor-in-Chief of SIAM Journal of Applied Dynamical Systems.
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