2015/10/31 by Reynaldo Castaneira, Instituto de Investigaciones en Matem&, Pablo Padilla +7
Engineering · Mathematics · Physics and Astronomy · #Action (physics) #Class (philosophy) #Combinatorics #Cosmology and Gravitation Theories #Differential equation #Euler equations #Functional equation #Homogeneous #Limit (mathematics) #Limiting #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Spacecraft Dynamics and Control #Type (biology) #Zero (linguistics) #math.DS
paper · pdf · doi:10.3842/sigma.2016.104
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
arxiv created 2016/10/31 · openalex publication_date 2016/10/31 · arxiv updated 2016/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the limit N + of N -body type problems with weak interaction, equal masses and --homogeneous potential, 0 < < 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 .