Dual Pairs and Regularization of Kummer Shapes in Resonances

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dc.contributor.authorOhsawa, Tomoki
dc.contributor.utdAuthorOhsawa, Tomoki
dc.date.accessioned2020-03-24T22:17:54Z
dc.date.available2020-03-24T22:17:54Z
dc.date.issued2019-06
dc.descriptionDue to copyright restrictions and/or publisher's policy full text access from Treasures at UT Dallas is not available. UTD affiliates may be able to acquire a copy through Interlibrary Loan by using the link to UTD ILL.
dc.description.abstractWe present an account of dual pairs and the Kummer shapes for n : m resonances that provides an alternative to Holm and Vizman’s work. The advantages of our point of view are that the associated Poisson structure on su(2)* is the standard (+)-Lie–Poisson bracket independent of the values of (n, m) as well as that the Kummer shape is regularized to become a sphere without any pinches regardless of the values of (n, m). A similar result holds for n : −m resonance with a paraboloid and su(1, 1)* . The result also has a straightforward generalization to multidimensional resonances as well. ©2019 American Institute of Mathematical Sciences
dc.description.departmentSchool of Natural Sciences and Mathematics
dc.identifier.bibliographicCitationOhsawa, T.. 2019. "Dual pairs and regularization of kummer shapes in resonances." Journal of Geometric Mechanics 11(2): 225-238, doi: 10.3934/jgm.2019012
dc.identifier.issn1941-4889
dc.identifier.issue2
dc.identifier.urihttp://dx.doi.org/10.3934/jgm.2019012
dc.identifier.urihttps://hdl.handle.net/10735.1/7474
dc.identifier.volume11
dc.language.isoen
dc.publisherAmerican Institute of Mathematical Sciences
dc.rights©2019 American Institute of Mathematical Sciences
dc.source.journalJournal of Geometric Mechanics
dc.subjectResonance
dc.subjectKummer surfaces
dc.titleDual Pairs and Regularization of Kummer Shapes in Resonances
dc.type.genrearticle

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