Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Syzygies for periodic orbits in the restricted three-body problem   In this paper we show the existence of syzygies for all periodic orbits
inside the bounded Hill's region of the planer circular restricted three-body
problem with energy below the second critical value. The proof will follow some
ideas of Birkhoff to compute the roots of partial derivatives of the effective
potential. Birkhoff's methods are extended to higher energies and a new base
case is created and shown to fulfil the requirements. An other step from
Birkhoff is scrutinized to continue the statement to all mass ratios. The final
step is achieved by integrating over periodic orbits. Applying the same methods
to Hill's lunar problem delivers similar results in that setting as well.

8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph