Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction
We consider the limit N→+∞ of N-body type problems with weak interaction, equal masses and −σ-homogeneous potential, 0<σ<1. We obtain the integro-differential equation that the motions must satisfy, with limit choreographic solutions corresponding to travelling waves of this equation. Such equ...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148005 |
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| Cite this: | Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction / R. Castaneira, P. Padilla, H. Sánchez-Morgado // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. |
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Castaneira, R. Padilla, P. Sánchez-Morgado, H. 2019-02-16T16:27:59Z 2019-02-16T16:27:59Z 2016 Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction / R. Castaneira, P. Padilla, H. Sánchez-Morgado // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70F45; 70G75; 70F10 DOI:10.3842/SIGMA.2016.104 https://nasplib.isofts.kiev.ua/handle/123456789/148005 We consider the limit N→+∞ of N-body type problems with weak interaction, equal masses and −σ-homogeneous potential, 0<σ<1. We obtain the integro-differential equation that the motions must satisfy, with limit choreographic solutions corresponding to travelling waves of this equation. Such equation is the Euler-Lagrange equation of a corresponding limiting action functional. Our main result is that the circle is the absolute minimizer of the action functional among zero mean (travelling wave) loops of class H¹. We would like to thank R. Montgomery and C. Garc´ıa Azpeitia for pointing out mistakes in earlier versions of the paper. R. Castaneira is grateful to R. Montogomery for all his support to visit him at UC Santa Cruz. The authors thank the referees for useful observations. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
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Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction Castaneira, R. Padilla, P. Sánchez-Morgado, H. |
| title_short |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_full |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_fullStr |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_full_unstemmed |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_sort |
continuous choreographies as limiting solutions of n-body type problems with weak interaction |
| author |
Castaneira, R. Padilla, P. Sánchez-Morgado, H. |
| author_facet |
Castaneira, R. Padilla, P. Sánchez-Morgado, H. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We consider the limit N→+∞ of N-body type problems with weak interaction, equal masses and −σ-homogeneous potential, 0<σ<1. We obtain the integro-differential equation that the motions must satisfy, with limit choreographic solutions corresponding to travelling waves of this equation. Such equation is the Euler-Lagrange equation of a corresponding limiting action functional. Our main result is that the circle is the absolute minimizer of the action functional among zero mean (travelling wave) loops of class H¹.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148005 |
| fulltext |
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| citation_txt |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction / R. Castaneira, P. Padilla, H. Sánchez-Morgado // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. |
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2025-11-24T09:17:23Z |
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2025-11-24T09:17:23Z |
| _version_ |
1850844525329645568 |