动力系统讨论班

 题目： Action and periodic orbits of area-preserving surface diffeomorphisms

 报告人：曲华迪（南方科技大学）

摘要：We are interested in the periodic points of area-preserving diffeomorphisms on surfaces. The celebrated Poincare-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 the positive developments by Hutchins in 2016 and Weiler in 2019, our work delves into a more precise examination of the dependency of quantitative results, further generalizing and unifying these two results. Our investigation involves two crucial invariants of surface diffeomorphisms: the mean action and the rotation vector defined on the invariant measure set. We reveals the intrinsic connection between these two invariants, leading to the formulation of a further conjecture that generalize the Poincare-Birkhoff theorem.

时间：2024年04月17日（周三）上午9:00-10:00

地点：永利3044官网本部新教二楼510教室

联系人：孙善忠