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arXiv · 2006.15369

The height invariant of a four-parameter semitoric system with two focus-focus singularities

Jaume Alonso·Sonja Hohloch
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Abstract

Semitoric systems are a special class of completely integrable systems with two degrees of freedom that have been symplectically classified by Pelayo and Vu Ngoc about a decade ago in terms of five symplectic invariants. If a semitoric system has several focus-focus singularities, then some of these invariants have multiple components, one for each focus-focus singularity. Their computation is not at all evident, especially in multi-parameter families. In this paper, we consider a four-parameter family of semitoric systems with two focus-focus singularities. In particular, apart from the polygon invariant, we compute the so-called height invariant. Moreover, we show that the two components of this invariant encode the symmetries of the system in an intricate way.

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Jaume Alonso, Sonja Hohloch. 2020-06-27. The height invariant of a four-parameter semitoric system with two focus-focus singularities. https://doi.org/10.1007/s00332-021-09706-4

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