Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hill-type formula and Krein-type trace formula for $S$-periodic
  solutions in ODEs   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.

29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci