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Stable and Chaotic Dynamics in Certain Quasi-periodically Forced Differential Equations

发布时间：2022-05-27 作者：浏览次数：

Speaker:	吕克宁	DateTime:	2022年5月30日（周一）上午10:00-11:00
Brief Introduction to Speaker: 吕克宁，教授，四川大学。		Place:	腾讯会议：233205833
Abstract:We study the complicated dynamics of quasi-periodically perturbed ordinary differential equations with a homoclinic orbit to a dissipative saddle point. We show that there are four regions of parameters in which the equations have respectively: (1) attracting quasi-periodic integral manifolds of Levinson type; (2) transition to chaos; (3) strange attractors;(4) homoclinic tangles. In the case of homoclinic tangles, we not only obtain the results on horseshoes similar to the existing ones, but also give a comprehensive geometric description of the structures of tangles. This is a joint work with Wen Huang and Qiudong Wang.