ACTION AND PERIODIC ORBITS OF AREA-PRESERVING SURFACE DIFFEOMORPHISMS
报告专家：曲华迪博士（南方科技大学）
报告时间：2024年9月5日（星期四）下午14：30-16：00
报告地点：数学学院南114 腾讯会议：557570523 密码：0905
报告摘要：We are interested in the periodic points of area-preserving diffeomorphisms on surfaces. The celebrated Poincaré-Birkhoff fixed point theorem and subsequent generalizations revealed the existence and abundance of periodic solutions in Hamiltonian systems, but the good structure of the collection of periodic solutions remains unknown.
Converting area-preserving surface diffeomorphisms to Reeb flow via open book decomposition provided a way to relate the dynamics of area-preserving surface diffeomorphisms and the dynamic of Reeb flows of 3-dimensional contact manifolds, and ECH (Embedded Contact Homology) theory proves to be powerful. Though this way ,we want to conduct a quantitative analysis about the distribution of periodic orbit, based on previous results，our work delves into a more precise examination of the dependency of quantitative results, further generalizing and unifying old results. Our investigation involves two crucial invariants of surface diffeomorphisms: the mean action and the rotation vector. We reveal the intrinsic connection between these two invariants, leading to the formulation of a further conjecture that generalize the Poincaré-Birkhoff theorem.
专家简介：曲华迪，南方科技大学博士，导师为美国西北大学夏志宏教授，现从事动力系统方向，具体为曲面上保面积映射周期轨道性质的研究。
邀请人：鄢敬之
