arXiv subjects

Yannick Gullentops

Publications and source records attributed to Yannick Gullentops.

2 recordsLinked to original sources

arXiv2023

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 manifolds that have an underlying $S^1$-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.

math.DS↗

arXiv2022

Creating hyperbolic-regular singularities in the presence of an $\mathbb{S}^1$-symmetry

On a 4-dimensional compact symplectic manifold, we study how suitable perturbations of a toric system to a family of completely integrable systems with $\mathbb{S}^1$-symmetry lead to various hyperbolic-regular singularities. We compute and visualise associated phenomena like flaps, swallowtails, and $k$-stacked tori for $k \in \{2, 3, 4\}$ and give an upper bound for $k$ in our family of systems.

math.DS↗