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arXiv · 1911.11883

A family of semitoric systems with four focus-focus singularities and two double pinched tori

Annelies De Meulenaere·Sonja Hohloch
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Abstract

We construct a 1-parameter family $F_t=(J, H_t)_{0 \leq t \leq 1}$ of integrable systems on a compact $4$-dimensional symplectic manifold $(M, ω)$ that changes smoothly from a toric system $F_0$ with eight elliptic-elliptic singular points via toric type systems to a semitoric system $F_t$ for $ t^- < t < t^+$. These semitoric systems $F_t$ have precisely four elliptic-elliptic and four focus-focus singular points. Moreover, at $t= \frac{1}{2}$, the system has precisely two focus-focus fibres each of which contains exactly two focus-focus points, giving these fibres the shape of double pinched tori. We exemplarily parametrise one of these fibres explicitly.

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Annelies De Meulenaere, Sonja Hohloch. 2019-12-20. A family of semitoric systems with four focus-focus singularities and two double pinched tori. https://arxiv.org/abs/1911.11883

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