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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 104, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.104
(Mi sigma1186)
 

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

Reynaldo Castaneiraa, Pablo Padillaa, Héctor Sánchez-Morgadob

a Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, UNAM, México D.F. 04510, México
b Instituto de Matemáticas, UNAM, México D.F. 04510, México
References:
Abstract: We consider the limit $N\to +\infty$ of $N$-body type problems with weak interaction, equal masses and $-\sigma$-homogeneous potential, $0<\sigma<1$. 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 $H^1$.
Keywords: $N$-body problem; continuous coreography; Lagrangian action.
Received: October 20, 2015; in final form October 29, 2016; Published online October 31, 2016
Bibliographic databases:
Document Type: Article
MSC: 70F45; 70G75; 70F10
Language: English
Citation: Reynaldo Castaneira, Pablo Padilla, Héctor Sánchez-Morgado, “Continuous Choreographies as Limiting Solutions of $N$-body Type Problems with Weak Interaction”, SIGMA, 12 (2016), 104, 9 pp.
Citation in format AMSBIB
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\by Reynaldo~Castaneira, Pablo~Padilla, H\'ector~S\'anchez-Morgado
\paper Continuous Choreographies as Limiting Solutions of $N$-body Type Problems with Weak Interaction
\jour SIGMA
\yr 2016
\vol 12
\papernumber 104
\totalpages 9
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\crossref{https://doi.org/10.3842/SIGMA.2016.104}
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