Multiple chaotic motions arising from a degenerate homoclinic orbit

主讲人：朱长荣  重庆大学教授

时间：2021年9月29日15：00

地点：腾讯会议701 215 905  密码：123456

举办单位：数理学院

主讲人介绍：朱长荣，重庆大学数学与统计学院教授，博士生导师。2000年考入重庆大学，攻读硕士学位；2004年考入四川大学攻读博士学位。现在主要从事微分方程与动力系统的研究。先后到意大利、加拿大等国访问。多次主持国家自然科学基金。研究结果发表在包括Ann. I. H. Poincare-AN、 J. Diff.  Eqns.、Nonlinearity、 Proc. Roy. Soc. Edinburgh Sect. A等多个有重要影响的国际期刊上。

内容介绍：In this talk, we consider multiple existence of homoclinic solutions for a  periodically perturbed $N$-dimensional autonomous differential equation with a  degenerate homoclinic solution of degeneracy degree $d$. Known results were  obtained with a functional perturbation, which is regarded as an  infinite-dimensional parameter. In this paper we prove that the single parameter  is enough to unfold all possibilities of linearly independent homoclinic  solutions bifurcated from the unperturbed degenerate homoclinic one, which  actually improves the known results. Furthermore,we prove that those homoclinic  solutions are all transversal, showing co-existence of multiple chaotic motions.