Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Authors: Castaneira, R., Padilla, P., Sánchez-Morgado, H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148005
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• 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.

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...