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періодичних видань НАН України
періодичних видань НАН України
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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| dc.contributor.author | Castaneira, R. | |
| dc.contributor.author | Padilla, P. | |
| dc.contributor.author | Sánchez-Morgado, H. | |
| dc.date.accessioned | 2019-02-16T16:27:59Z | |
| dc.date.available | 2019-02-16T16:27:59Z | |
| dc.date.issued | 2016 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2010 Mathematics Subject Classification: 70F45; 70G75; 70F10 | |
| dc.identifier.other | DOI:10.3842/SIGMA.2016.104 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/148005 | |
| dc.description.abstract | 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. | uk_UA |
| dc.description.sponsorship | 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. | 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 | Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
