Periods of the Goldfish Many-Body Problem

Abstract

Calogero’s goldfish N-body problem describes the motion of N point particles subject to mutual interaction with velocity-dependent forces under the action of a constant magnetic field transverse to the plane of motion. When all coupling constants are equal to one, the model has the property that for generic initial data, all motions of the system are periodic. In this paper we investigate which are the possible periods of the system for fixed N, and we show that there exist initial data that realize each of these possible periods. We then discuss the asymptotic behaviour of the maximal period for large particle number N.