Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global hypersurfaces of section in the spatial restricted three-body
  problem   We propose a contact-topological approach to the spatial circular restricted
three-body problem, for energies below and slightly above the first critical
energy value. We prove the existence of an $S^1$-family of global hypersurfaces
of section for the regularized dynamics, which are copies of
$(\mathbb{D}^*S^2,\omega)$, where $\omega$ is deformation equivalent to the
standard symplectic form. This is the page of an open book in $S^*S^3=S^3\times
S^2$, with binding $S^*S^2=\mathbb{R}P^3$, and the situation at the binding
reduces to the planar problem. The first return map is Hamiltonian, restricting
to the boundary as the time-$1$ map of a positive reparametrization of the Reeb
flow in $\mathbb{R}P^3$ giving the planar problem. This construction holds for
any choice of mass ratio, and is therefore non-perturbative. We illustrate the
technique in the completely integrable case of the rotating Kepler problem,
where the return map can be studied explicitly.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an