Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

 Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Professor Holger Dullin
Univerität Sydney und TUM München
 
spricht am
 
Montag, 5. November 2018
 
um
 
16:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»On symplectic invariants of Liouville foliations«

Abstract:
The Taylor series invariant of a focus-focus point in a semi-toric systems with two degrees of freedom is a symplectic invariant of its Liouville foliation. I will present an example that is obtained from reduction of the harmonic oscillator in 4 dimensions that is related to the Kepler problem, which leads to a family of integrable system on S^2 \times S^2. After singular reduction to one degree of freedom the computation of the invariants is based on the analysis of complete Abelian integrals. In this family there is a transition from a semi-toric system to a toric system which is the Hamiltonian Hopf bifurcation. I will describe how a different type of the same bifurcation leads to a transition from semi-toric system to an integrable system with hyperbolic singularities, for which a global classification theory is still missing.

 

Hierzu ergeht herzliche Einladung.
Urs Frauenfelder
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).


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