A multi-particle McMillan integrable symplectic map
报告题目(Title)：A multi-particle McMillan integrable symplectic map
报告人(Speaker)：周汝光 教授（江苏师范大学）
地点(Place)：后主楼1328
时间(Time)：2026年4月13日（周一）10:00-11:00
邀请人(Inviter)：王灯山
报告摘要
The McMillan map, introduced by Edwin McMillan in 1971, serves as a fundamental model for the nonlinear dynamics of particles in synchrotron storage rings. Renowned for its elegant mathematical structure and practical relevance to accelerator physics, the map has been extensively studied. A significant advancement occurred in 2014, when Danilov and Nagaitsev developed a multi-particle generalization consisting of identical particles. In this talk, we introduce a novel multi-particle generalization of the McMillan map that incorporates non-identical particles. We rigorously prove the integrability and symplecticity of the system by establishing its discrete Lax representation, where the Lax matrix satisfies the classical r-matrix relations. Furthermore, we demonstrate that this map is intimately connected to the Kaup–Newell hierarchy. We investigate the analytic properties and asymptotic behaviors of the common eigenfunctions—associated with both the Lax equation and the discrete-time spectral problem—near the points at infinity on the complex plane. By introducing root variables and employing Abel–Jacobi coordinates, we show that the discrete-time evolution is linearized into a linear flow on the associated Jacobi variety. Finally, we construct explicit algebro-geometric solutions for the map in terms of Riemann theta functions.
主讲人简介
周汝光，江苏师范大学数学与统计学院教授、博士生导师，曾任江苏师范大学校长，现任教育部高等学校数学类专业教学指导委员会委员。1997年在复旦大学获得基础数学方向理学博士学位，长期从事可积系统的数学理论研究，博士论文被评为2000年全国优秀博士学位论文。2001—2002年在德国帕德博恩大学担任洪堡学者。曾参与国家攀登计划“非线性科学”项目及国家重点基础研究发展规划项目“非线性科学中的若干前沿问题”项目各1项，主持完成国家自然科学基金项目6项。入选教育部“新世纪优秀人才支持计划”。研究成果获教育部自然科学二等奖。
