时间：2019年11月2日（星期六）10:00-11:00

地点：勤园21 号306报告厅

主讲人：张祥，上海交通大学特聘教授（博士生导师、二级教授、享受国务院特殊津贴专家），欧洲科学与艺术院院士。曾获教育部新世纪优秀人才、上海市曙光学者和上海市浦江学者。 主要从事动力系统的定性、分支和可积理论的研究。所得结果部分解决了动力系统领域长期遗留的困难的公开问题和猜想，主要结果发表在American J. Math., Trans. Amer. Math. Soc., Comm. Math. Phys., J. Functional Analysis, J. Nonlinear Sciences 和J. Differential Equations等国际一流期刊上, 出版专著1部，教材1部，多次主持国家自然科学基金项目。 目前担任中国数学会奇异摄动专业委员会主任、中国数学会理事，以及国际SCI期刊Qualitative Theory of Dynamical Systems和International J. Bifurcation and Chaos的Associate编委等。

内容简介：In this talk we introduce our recent results on the period function of planar Hamiltonian differential systems with separable variables. More concretely we are concerned with the search of sufficient conditions implying the monotonicity of the period function, i.e., the absence of critical periodic orbits. We are also interested in the uniqueness problem and in this respect we seek conditions implying that there exists at most one critical periodic orbit. We obtain in a unified way several sufficient conditions that already appear in the literature, together with some other results that to the best of our knowledge are new. Finally we also investigate the limit of the period function as the periodic orbits tend to the boundary of the period annulus of the center.