应兰州大学数学与统计学院邀请，大湾区大学理学院赵志豪博士将于2025年 月 日举行线上学术报告。

报告题目: 哈密顿系统的P对称次调和闸轨道和 Maslov 指标

时 间：9月25日（星期四）19：00

腾讯会议 ID：706 158 141

报告摘要：This talk investigates subharmonic solutions of a Hamiltonian system that possess two key properties: P-symmetry and reversibility, which exhibit a symmetry group isomorphic to a dihedral group. These dihedral groups hold particular significance in various branches of physics, especially celestial mechanics and quantum Hamiltonian systems.

In this talk, we introduce relative-Morse index estimates for such subharmonic (P-symmetric brake) solutions via the Saddle-point Theorem and Galerkin approximation. Moreover, we develop a novel iteration theory for the Maslov-type (L, P)-index of symplectic paths, with applications to P-symmetric brake solutions in Hamiltonian systems. Under super-quadratic growth assumptions, we establish a criterion to distinguish solutions based on their periods. This result generalizes earlier work on brake orbits and provides a unified framework for analyzing symmetric Hamiltonian dynamics. Key tools include the Bott-type iteration formula for the (L, P)-index and spectral flow. This is joint work with Prof. Duanzhi Zhang.

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报告人简介

赵志豪博士，现在大湾区大学从事博士后研究，合作导师是段金桥教授。2023年博士毕业于南开大学，博士导师张端智教授。研究方向是哈密顿系统，结合变分法、Maslov指标迭代理论研究哈密顿系统的次调和解，Lagrange边值解和极小周期解的适定性问题；研究哈密顿系统（周期）边值解的变分分岔和线性稳定性理论，及在随机动力系统最可能迁移道路问题中的应用等。目前主持国家自然科学基金一项。在JDE，DCDS-A等期刊发表3篇文章。

数学与统计学院

甘肃应用数学中心

萃英学院

2025年9月22日