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arXiv · 1504.01815

Hill-type formula and Krein-type trace formula for $S$-periodic solutions in ODEs

Xijun Hu·Penghui Wang
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Abstract

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 \cite{HOW}. 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 \cite{HOW}. 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 \cite{HOW}, 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.

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Xijun Hu, Penghui Wang. 2015-04-08. Hill-type formula and Krein-type trace formula for $S$-periodic solutions in ODEs. https://arxiv.org/abs/1504.01815

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