报告时间：2026年6月29日（周一）上午 10:00-11:00
报告地点：苏州大学天赐庄校区精正楼306
报告人：刘磊 副研究员，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 first 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 constraints 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. As a second step, this result admits a qualitative dynamical interpretation via the open book decomposition by 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. Refining Hutchings' mean action inequality, we prove that every rational number in the interior of the twist interval is realized as the mean relative winding number of two distinct periodic points of the first return map. For energies above the critical level, where the energy surface is non-compact, we prove the existence of infinitely many periodic orbits and infinitely many parabolic trajectories via twist estimates near infinity. This is joint work with Xijun Hu, Yuwei Ou, Zhiwen Qiao and Pedro A. S. Salomão.
报告人简介：
刘磊，山东大学永利皇宫 副研究员，分别于哈尔滨工程大学、山东大学取得本科、博士学位，博士导师为胡锡俊教授。曾在北京大学国际数学研究中心从事博士后研究，合作导师为田刚院士。主要研究方向为辛几何与动力系统，包括闭特征问题，闭测地线问题，N体问题等，研究成果发表于JEMS，CMP，JDE，JDDE，DCDS，Front. Math.等国际期刊。
邀请人：董自康