Sonja Hohloch - On recent advances in semitoric integrable systems

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Sonja Hohloch (University Antwerpen)


On recent advances in semitoric integrable systems



Roughly speaking, a semitoric system is a completely integrable Hamiltonian system on a 4-dimensional symplectic manifold that admits only nondegenerate singularities without hyperbolic components and whose flow gives rise to an $(\mathbb S^1 \times \mathbb R)$-action. Coupled spin oscillators and coupled angular momenta are examples of such semitoric systems.
Semitoric systems have been symplectically classified about a decade ago by Pelayo $\&$ Vu Ngoc by means of five invariants. Recently, there has been made considerable progress by various authors concerning the computation of these invariants.
In this talk, we will give an introduction to semitoric systems before considering a recent, intuitive family of semitoric systems that allows for explicit observation of bifurcation behaviour such as bifurcations between focus-focus and elliptic-elliptic singularities and other interesting geometric-topological features related to singularities and bifurcations. The latter part is based on a joint work with A. De Meulenaere.
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