Besides three-dimensional autonomous nonlinear dynamical systems, periodically driven nonlinear oscillators constitute elementary classes of systems that can potentially exhibit chaotic behavior. In this contribution we investigate conditions on the shape of the potential and the functional form of the periodic driving that are necessary for the occurrence of chaotic behavior in these systems by deriving analytical criteria that exclude chaotic long-time solutions.

PACS numbers: 05.45.Ac, 02.30.Hq, 05.90.+m