Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the period of the periodic orbits of the restricted three body
  problem   We will show that the period $T$ of a closed orbit of the planar circular
restricted three-body problem (viewed on rotating coordinates) depends on the
region it encloses. Roughly speaking, we show that, $2 T=k\pi+\int_\Omega g$
where $k$ is an integer, $\Omega$ is the region enclosed by the periodic orbit
and $g:\mathbb{R}^2\to \mathbb{R}$ is a function that only depends on the
constant $C$ known as the Jacobian integral; it does not depend on $\Omega$.
This theorem has a Keplerian flavor in the sense that it relates the period
with the space "swept" by the orbit. As an application, we prove that there is
a neighborhood around $L_4$ such that every periodic solution contained in this
neighborhood must move clockwise. The same result holds true for $L_5$.

10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin