Integrable Flows for Starlike Curves in Centroaffine Space

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Фізико-технічні та математичні науки
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Відділення математики
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9, випуск за цей рік
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dc.contributor.author	Calini, A.
dc.contributor.author	Ivey, T.
dc.contributor.author	Beffa, G.M.
dc.date.accessioned	2019-02-19T19:00:46Z
dc.date.available	2019-02-19T19:00:46Z
dc.date.issued	2013
dc.identifier.citation	Integrable 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.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 37K10; 53A20; 53C44
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2013.022
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149224
dc.description.abstract	We 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.sponsorship	This 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.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Integrable Flows for Starlike Curves in Centroaffine Space	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA