报告题目：Persistence of Lower Dimensional Degenerate Invariant Tori with Prescribed Frequencies in Hamiltonian Systems with Small Parameter

报告简介：In this paper we develop some KAM technique to prove the persistence of lower dimensional elliptic-type degenerate invariant tori with prescribed frequencies in Hamiltonian systems. The proof is based on a formal KAM theorem with parameters, which enable us to solve equilibrium and choose parameter for small divisor conditions after the KAM iteration, instead in KAM steps. Moreover, it also depends on the existence of a connected path of real roots of approximating odd-degree real polynomials depending on parameter, which makes it possible to tackle the Melnikov's conditions.

报告人：徐君祥，东南大学数学学院，教授、博导。长期从事哈密顿系统，可逆系统和拟周期系统的KAM理论问题研究，取得了一些有意义的成果。在Russmann非退化条件，Melnikov非共振条件，退化KAM环面 等问题方面都取得了有意义的结果。有关成果发表在 Math. Z, J. Math. Pures. Appl,., JDE,., Ergod. Th. Dynam. Sys.等重要学术期刊上。最近从事退化拟周期问题的研究，也已经取得了一些有意义的结果。有关成果曾获得了2018年度教育部自然科学二等奖。

报告时间：2022年3月27日(周日) 14: 00-15: 30

报告地点：腾讯会议，ID：465542611

主办单位：扬州大学数学科学学院、扬州大学科技处

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