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...
Збережено в:
| Дата: | 2013 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149224 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-149224 |
|---|---|
| record_format |
dspace |
| fulltext |
|
| spelling |
nasplib_isofts_kiev_ua-123456789-1492242025-02-09T22:10:48Z Integrable Flows for Starlike Curves in Centroaffine Space Calini, A. Ivey, T. Beffa, G.M. 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. 2013 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Calini, A. Ivey, T. Beffa, G.M. |
| spellingShingle |
Calini, A. Ivey, T. Beffa, G.M. Integrable Flows for Starlike Curves in Centroaffine Space Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Calini, A. Ivey, T. Beffa, G.M. |
| author_sort |
Calini, A. |
| title |
Integrable Flows for Starlike Curves in Centroaffine Space |
| title_short |
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_sort |
integrable flows for starlike curves in centroaffine space |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149224 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT calinia integrableflowsforstarlikecurvesincentroaffinespace AT iveyt integrableflowsforstarlikecurvesincentroaffinespace AT beffagm integrableflowsforstarlikecurvesincentroaffinespace |
| first_indexed |
2025-12-01T08:11:43Z |
| last_indexed |
2025-12-01T08:11:43Z |
| _version_ |
1850292781603356672 |