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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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Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction
Інший ID:
2010 Mathematics Subject Classification: 70F45; 70G75; 70F10
DOI:10.3842/SIGMA.2016.104
DOI:10.3842/SIGMA.2016.104
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
534
Завантажень:
222
Анотація:
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.
