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

Yannick Gullentops; Sonja Hohloch

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

Dynamical Systems 2022-10-03 v1 Symplectic Geometry Exactly Solvable and Integrable Systems

Authors: Yannick Gullentops , Sonja Hohloch

Abstract

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.

Keywords

symplectic manifold toric system integrable systems hyperbolic-regular singularities s1-symmetry

Cite

@article{arxiv.2209.15631,
  title  = {Creating hyperbolic-regular singularities in the presence of an $\mathbb{S}^1$-symmetry},
  author = {Yannick Gullentops and Sonja Hohloch},
  journal= {arXiv preprint arXiv:2209.15631},
  year   = {2022}
}

Comments

44 pages, 22 figures

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

Abstract

Keywords

Cite

Comments

Related papers