Recent Examples of Hypersemitoric Systems and First Steps Towards a Classification: A Brief Survey

Hypersemitoric systems are 2-degree-of-freedom integrable systems on 4-dimensional symplectic manifolds that have an underlying \(\mathbb S^1\) -symmetry and no degenerate singularities apart from maybe a finite number of families of so-called parabolic singularities. We give a short overview of recent examples displaying various bifurcations and sketch a topological-combinatorial classification of the connected components of fibers of hypersemitoric systems.