Publication:
Classification of second-order conformally-superintegrable systems
Classification of second-order conformally-superintegrable systems
dc.contributor.advisor | Kress, Jonathan | en_US |
dc.contributor.author | Capel, Joshua | en_US |
dc.date.accessioned | 2022-03-21T14:01:54Z | |
dc.date.available | 2022-03-21T14:01:54Z | |
dc.date.issued | 2014 | en_US |
dc.description.abstract | Over the last half century the study of superintegrable systems has established itself as an interesting subject with connections to some of the earliest known dynamical systems in mathematical-physics. Systems with constants second-order in the momenta have been particularly well studied in recent years. This thesis provides a classification of non-degenerate (maximum parameter) three-dimensional second-order superintegrable systems over conformally-flat spaces. I show that, up to Staeckel equivalence, such systems can be put into correspondence with a 6 points in the extended complex plane with an action induced by the conformal-group in three dimensions. I use this correspondence, and the tools of classical-invariant theory, to determine the inequivalent orbits under this action and show there are only 10 conformal-classes. This answers an open problem by showing that no unknown systems exist on the sphere. Additional interest in these systems comes from studying their algebra of constants. In the three-dimensional maximum-parameter case this algebra is generated by the iterated Poisson brackets of the 6 linearly independent second-order constants and is known to close at finite order. These 6 second-order constants are necessarily functionally dependent, and up to now the explicit relation for their dependence has only been known on a case-by-case basis. In this thesis I demonstrate a quartic identity which provides the functional relation for a general system. | en_US |
dc.identifier.uri | http://hdl.handle.net/1959.4/53501 | |
dc.language | English | |
dc.language.iso | EN | en_US |
dc.publisher | UNSW, Sydney | en_US |
dc.rights | CC BY-NC-ND 3.0 | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/au/ | en_US |
dc.subject.other | Representation Theory | en_US |
dc.subject.other | Superintegrability | en_US |
dc.subject.other | Mathematical Physics | en_US |
dc.title | Classification of second-order conformally-superintegrable systems | en_US |
dc.type | Thesis | en_US |
dcterms.accessRights | open access | |
dcterms.rightsHolder | Capel, Joshua | |
dspace.entity.type | Publication | en_US |
unsw.accessRights.uri | https://purl.org/coar/access_right/c_abf2 | |
unsw.identifier.doi | https://doi.org/10.26190/unsworks/16817 | |
unsw.relation.faculty | Science | |
unsw.relation.originalPublicationAffiliation | Capel, Joshua, Mathematics & Statistics, Faculty of Science, UNSW | en_US |
unsw.relation.originalPublicationAffiliation | Kress, Jonathan, Mathematics & Statistics, Faculty of Science, UNSW | en_US |
unsw.relation.school | School of Mathematics & Statistics | * |
unsw.thesis.degreetype | PhD Doctorate | en_US |
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