[Distinguished Lecture] Response solutions in degenerate, quasi-periodically forced nonlinear oscillators

For a quasi-periodically forced differential equation, response solutions are quasi-periodic ones whose frequency vector coincides with that of the forcing function and they are known to play a fundamental role in the harmonic and synchronizing behaviors of quasi-periodically forced oscillators. These solutions are well-understood in quasi-periodically perturbed nonlinear oscillators either in the presence of large damping or in the non-degenerate cases with small or free damping. This talk will present some recent results on the existence of responsive solutions in degenerate, quasi-periodically forced nonlinear oscillators with small or free damping. The case with noise perturbation will also be discussed.