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A family of compact semitoric systems with two focus-focus singularities

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About 6 years ago, semitoric systems were classified by Pelayo & Vu Ngoc by means of five invariants. Standard examples are the coupled spin oscillator on S-2 x R-2 and coupled angular momenta on S-2 x S-2, both having exactly one focus-focus singularity. But so far there were no explicit examples of systems with more than one focus-focus singularity which are semitoric in the sense of that classification. This paper introduces a 6-parameter family of integrable systems on S-2 x S-2 and proves that, for certain ranges of the parameters, it is a compact semitoric system with precisely two focus-focus singularities. Since the twisting index (one of the semitoric invariants) is related to the relationship between different focus-focus points, this paper provides systems for the future study of the twisting index.
Tijdschrift: Journal of Geometric Mechanics
ISSN: 1941-4889
Volume: 10
Pagina's: 331 - 357
Jaar van publicatie:2018
Trefwoorden:A1 Journal article
BOF-keylabel:ja
BOF-publication weight:1
CSS-citation score:2
Auteurs:International
Authors from:Higher Education
Toegankelijkheid:Open