黄色仓库

报告时间：2026年4月12日（周日）上午 09:30-10:30

报告地点：黄色仓库 纯水楼301

报告人：胡锡俊 教授，山东大学

报告摘要：

We study dynamical constraints arising from Embedded Contact Homology (ECH) in the spatial isosceles three-body problem. For energies below the critical level, the dynamics on the energy surface is identified with a Reeb flow on the tight three-sphere. We obtain quantitative estimates for the Euler orbit, including monotonicity of its transverse rotation number and a strict inequality comparing its action with the contact volume. Combined with the ECH classification of Reeb flows on the tight three-sphere with two simple periodic orbits, these estimates rule out the two-orbit scenario, thus forcing every compact energy surface below the critical level to have infinitely many periodic orbits. The result admits a dynamical interpretation via disk-like global surfaces of section bounded by the Euler orbit. In this setting, the rotation number and the contact volume define a non-trivial twist interval which encodes the relative winding of periodic orbits.

This talk is based on joint works with Lei Liu, Yuwei Ou, Zhiwen Qiao, Pedro A. S. Salomão, and Guowei Yu.

报告人简介：

胡锡俊，山东大学特聘教授，博士生导师。国家杰出青年基金获得者。曾获教育部自然科学一等奖，入选山东省泰山学者攀登计划。主要研究方向为动力系统与非线性泛函分析。在N体问题，哈密顿系统指标理论及反应-扩散方程的研究中做出了创新性的工作。

邀请人：杨大伟