Splay-Phase Orbits for Equivariant Flows on Tori

This paper studies dynamical systems on the n-fold torus equivariant under a cyclic permutation of coordinates. It is proved that under a mild condition, these systems have splay-phase solutions. These are periodic orbits in which the n coordinates are given by the same function of time, but equally separated in phase. Applications to systems of equations used to model Josephson junction arrays are discussed.