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

Reynaldo Castaneira, Pablo Padilla, Héctor Sánchez-Morgado

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 equat…