Integrable Flows for Starlike Curves in Centroaffine Space
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 hierarch...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2013 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149224 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862643438853292032 |
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| author | Calini, A. Ivey, T. Beffa, G.M. |
| author_facet | Calini, A. Ivey, T. Beffa, G.M. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-01T08:11:43Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149224 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T08:11:43Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Calini, A. Ivey, T. Beffa, G.M. 2019-02-19T19:00:46Z 2019-02-19T19:00:46Z 2013 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. 1815-0659 2010 Mathematics Subject Classification: 37K10; 53A20; 53C44 DOI: http://dx.doi.org/10.3842/SIGMA.2013.022 https://nasplib.isofts.kiev.ua/handle/123456789/149224 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrable Flows for Starlike Curves in Centroaffine Space Article published earlier |
| spellingShingle | Integrable Flows for Starlike Curves in Centroaffine Space Calini, A. Ivey, T. Beffa, G.M. |
| title | Integrable Flows for Starlike Curves in Centroaffine Space |
| title_full | Integrable Flows for Starlike Curves in Centroaffine Space |
| title_fullStr | Integrable Flows for Starlike Curves in Centroaffine Space |
| title_full_unstemmed | Integrable Flows for Starlike Curves in Centroaffine Space |
| title_short | Integrable Flows for Starlike Curves in Centroaffine Space |
| title_sort | integrable flows for starlike curves in centroaffine space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149224 |
| work_keys_str_mv | AT calinia integrableflowsforstarlikecurvesincentroaffinespace AT iveyt integrableflowsforstarlikecurvesincentroaffinespace AT beffagm integrableflowsforstarlikecurvesincentroaffinespace |