Degenerate Resonances and Synchronization of Quasiperiodic Oscillations

We consider quasiperiodic nonconservative perturbations of two-dimensional nonlinear Hamiltonian systems. We introduce the notion of a degenerate resonance and study the topology of a degenerate resonance zone with odd and even orders of degeneracy. A special attention is paid the oscillation synchronization while an invariant torus is passing through the resonance zone. We establish the existence of synchronization intervals with respect to a control parameter. The study is based on the analysis of a pendulum–type averaged system determining the dynamics in the resonance zone.