标题：Hill-type formula for Hamiltonian system with Lagrangian boundary conditions
作者：Hu, Xijun; Ou, Yuwei; Wang, Penghui
作者机构：[Hu, Xijun; Wang, Penghui] Shandong Univ, Dept Math, Jinan, Shandong, Peoples R China.; [Ou, Yuwei] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai, Guang 更多
通讯作者地址：[Ou, YW]Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai, Guangdong, Peoples R China.
来源：JOURNAL OF DIFFERENTIAL EQUATIONS
关键词：Hill-type formula; Trace formula; Conditional Fredholm determinant;; Linear stability; Planar 3-body problem
摘要：In this paper, we build up Hill-type formula for linear Hamiltonian systems with Lagrangian boundary conditions, which include standard Neumann, Dirichlet boundary conditions. Such a kind of boundary conditions comes from the N-reversible symmetry periodic orbits in n-body problem naturally, where N is an anti-symplectic orthogonal matrix with N-2 = I. The Hill-type formula connects the infinite determinant of the Hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions. Consequently, we derive the Krein-type trace formula and give nontrivial estimation for the eigenvalue problem. Combined with the Maslov-type index theory, we give some new stability criteria for the N-reversible symmetry periodic solutions of Hamiltonian systems. As an application, we study the linear stability of elliptic relative equilibria in planar 3-body problem. (C) 2019 Elsevier Inc. All rights reserved.