报告题目：Persistence of degenerate lower dimensional invariant tori with prescribed frequencies in Hamiltonian systems

报告人：徐君祥教授  东南大学

报告时间：2018年11月2日15:00-16:00

报告地点：知新楼B1044

摘要：In this paper we first study the stability of degenerate critical points of analytic functions. By analyzing isolation of critical points, we prove that there exists a critical point of minimum which can persist under small perturbations, moreover, the persisting critical point is still a minimum point and has the same stability under much smaller perturbations. Then, combining with some KAM technique, we prove the persistence of two classes of hyperbolic-type degenerate lower dimensional  invariant tori with prescribed frequencies under small perturbations.

报告人简介：

徐君祥，从事哈密顿系统与KAM理论研究，在哈密顿系统，拟周期系统，可逆系统，KAM理论，偏微分方程和临界点理论方面都有深入的研究，取得许多重要的科研成果.在Russmann非退化条件，较弱非共振条件的KAM定理，拟周期系统的约化问题， KAM环面Gevrey光滑的问题，具有退化平衡点的拟周期问题，偏微方程的基态解和同宿轨问题等方面取得一些有意义的结果。许多论文发表在一些重要的国际学术刊物，如 Math.Z.，J. Diff. Equa.，J. Math. Pures Appl., Ergod. Th. & Dynam. Sys., SIAM J. Math. Anal., Proc. Amer. Math. Soc. 等等。主持完成多项国家自然基金面上项目。

邀请人：司建国