Bifurcations from a degenerate homoclinic orbit

讲座时间 Datetime: 2022年6月17日，星期五，14:30—15:30

地点 Venue: 腾讯线上会议：636-229-235

 主持人 Host：王少卿

报告人 Speaker:朱长荣

单位 Affiliation:重庆大学

报告摘要 Abstract:

Consider an autonomous ordinary differential equation in R that has a  homoclinic solution asymptotic to a hyperbolic equilibrium. The homoclinic solution is degenerate in the sense that the linear variational equation has d bounded, linearly independent solutions. We study bifurcation of the homoclinic solution under periodic perturbations. Using exponential dichotomies and Lyapunov-Schmidt reduction, we obtain general conditions under which the perturbed system can have transverse homoclinic solutions and nearby periodic or chaotic solutions.