Universität Augsburg

Dr. Agustín Moreno
Universität Augsburg
spricht am
Montag, 4. Mai 2020
um
16:00 Uhr
im
Zoom
über das Thema:
Abstract: 
The search for closed orbits in the planar case of the restricted threebody problem goes back to groundbreaking work in celestial mechanics by Poincaré. His approach was to reduce the problem to: (i) Finding a global surface of section for the dynamics; (ii) Proving a fixed point theorem for the arising first return map (a “twist map”). This is the setting of the celebrated PoincaréBirkhoff theorem. In this talk, I will try to outline a generalization of this program to the spatial case (where the small mass is allowed to move in all threespace rather than on a plane). In particular, I will explain what is the replacement of a global surface of section, propose a generalization of the twist condition, and tackle the fixed point theory of these generalized twist maps. As an application, we expect these methods to provide the existence of simple spatial orbits of arbitrary long periods, generalizing a result by Conley to the spatial case. This is work in progress with Otto van Koert (Seoul National University). 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Kai Cieliebak 