Integrable Flows for Starlike Curves in Centroaffine Space

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dc.contributor.authorCalini, A.
dc.contributor.authorIvey, T.
dc.contributor.authorBeffa, G.M.
dc.date.accessioned2019-02-19T19:00:46Z
dc.date.available2019-02-19T19:00:46Z
dc.date.issued2013
dc.description.abstractWe construct integrable hierarchies of flows for curves in centroaffine R³ through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in RP² induces the Kaup-Kuperschmidt hierarchy at the curvature level.uk_UA
dc.description.sponsorshipThis paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. The authors would like to acknowledge the careful and detailed work of the anonymous referees in helping improve this paper. The authors also gratefully acknowledge support from the National Science Foundation: A. Calini through grants DMS-0608587 and DMS-1109017, and as a current NSF employee; T. Ivey through grant DMS-0608587; and G. Mar´ı Bef fa through grant DMS-0804541. T. Ivey also acknowledges support from the College of Charleston Mathematics Department. G. Mar´ı Bef fa also acknowledges the support of the Simons Foundation through their Fellows program.uk_UA
dc.identifier.citationIntegrable Flows for Starlike Curves in Centroaffine Space / A. Calini, T. Ivey, G.M. Beffa // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 30 назв. — англ.uk_UA
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 37K10; 53A20; 53C44
dc.identifier.otherDOI: http://dx.doi.org/10.3842/SIGMA.2013.022
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/149224
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleIntegrable Flows for Starlike Curves in Centroaffine Spaceuk_UA
dc.typeArticleuk_UA

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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9, випуск за цей рік