Abstract. 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.

嘉宾简介：

Yingfei Yi现为加拿大阿尔伯塔大学的Killam Memorial Chair教授，主要从事动力系统和微分方程的理论和应用的研究。他的工作涉及随机微分方程、哈密顿系统理论和遍历论等领域。主要成果发表在如 Ann. Probab., Comm. Math. Phys., Comm. Pure Appl. Math., Mem. Amer. Math. Soc.等国际重要期刊上。Yingfei Yi教授目前担任J. Dynam. Diff. Eqns杂志主编, 以及JDE等杂志的编委等。