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On the Stability of the 3-Body Problem (in 4D)

Webinar Presented By:  Professor Holger Dullin, School of Mathematics and Statistics, University of Sydney, Australia

Speaker Bio: Holger Dullin is a Professor in the School of Mathematics and Statistics at the University of Sydney.  His research interests are Dynamical Systems and Mathematical Physics, ranging from classical to quantum, from ODEs to PDEs, from integrable to chaotic, and from pure mathematics to real world applications. Recent highlights include contributions to the classification of integrable systems and new insights into the non-rigid body dynamics of springboard diving.

Abstract:  In 1998, at the ICM in Berlin, Michael Herman formulated what he called the "oldest problem in dynamics": Is the set of unbounded orbits in the 3-body problem dense for negative energies?  I will explain the background of this question, and then present recent results obtained jointly with Albouy and Scheurle that show that the answer to this question is "No." The catch is that our results hold for the 3-body problem in 4-dimensional space, but do not transfer to the usual setting in 2- or 3-dimensional space. The main observation is that for 3 bodies in dimension 4 there are simple periodic solutions (relative equilibria) at which the symmetry reduced Hamiltonian has a minimum. The ultimate reason is the structure of the rotational symmetry group SO(d) for different dimensions d.

Date and Time:  November 20, 2020 | 4:00 p.m. Eastern Time (US and Canada)

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