We present the calculation of Ruelle’s rotation number (frequency) Ω for a chain of damped and driven coupled Duffing oscillators using the recently discovered symplectic structure of the system. A relation between the eigenvalues of periodic orbits and the winding number ‖Ω‖/ω is conjectured by making use of their Krein signatures. The occurrence and nonoccurrence of plateaus with respect to the driving frequency ω can be explained via this relation.

• Received 8 February 1990

DOI:https://doi.org/10.1103/PhysRevA.41.6702