# Universität AugsburgInstitut für Mathematik

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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