Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Dr. Agustín Moreno
Universität Augsburg

 
spricht am
 
Montag, 4. Mai 2020
 
um
 
16:00 Uhr
 
im
 
Zoom
 
über das Thema:
 

»Long orbits in the spatial restricted three-body problem«

Abstract:
The search for closed orbits in the planar case of the restricted three-body 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 Poincaré-Birkhoff 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 three-space 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



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