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Title
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A family of compact semitoric systems with two focus-focus singularities
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Author
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Abstract
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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. |
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Language
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English
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Source (journal)
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Journal of Geometric Mechanics
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Publication
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2018
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ISSN
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1941-4889
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DOI
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10.3934/JGM.2018012
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Volume/pages
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10
:3
(2018)
, p. 331-357
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ISI
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000443308200003
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Full text (Publisher's DOI)
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Full text (open access)
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