标题：HILL-TYPE FORMULA AND KREIN-TYPE TRACE FORMULA FOR S-PERIODIC SOLUTIONS IN ODES
作者：Hu, Xijun; Wang, Penghui
作者机构：[Hu, Xijun; Wang, Penghui] Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China.
会议名称：2013 Workshop on Variational Problems and Evolution Equations
会议日期：JUL 22-25, 2013
来源：DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
关键词：Hill-type formula; Krein-type trace formula; Fredholm determinant;; Hilbert-Schmidt operator; S-periodic orbits
摘要：The present paper is devoted to studying the Hill-type formula and Krein-type trace formula for ODE, which is a continuous work of our previous work for Hamiltonian systems . Hill-type formula and Krein-type trace formula are given by Hill at 1877 and Krein in 1950's separately. Recently, we find that there is a closed relationship between them . In this paper, we will obtain the Hill-type formula for the S-periodic orbits of the first order ODEs. Such a kind of orbits is considered naturally to study the symmetric periodic and quasi-periodic solutions. By some similar idea in , based on the Hill-type formula, we will build up the Krein-type trace formula for the first order ODEs, which can be seen as a non-self-adjoint version of the case of Hamiltonian system.