Instability of the periodic motion of a particle interacting with a scalar wave field (Q1290996)

The system of equations which describe the motion of a classical particle interacting with a scalar wave field is considered. It is assumed that the linearization of the system around an equilibrium point has a single eigenvalue embedded in the continuous spectrum. It is proved that any eigenvector corresponding to this eigenvalue is unstable to perturbation through nonlinearity. The proof is based on the ideas of \textit{I. M. Sigal} [Commun. Math. Phys. 153, 297-320 (1993; Zbl 0780.35106)].