Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euler integral as a source of chaos in the three-body problem   In this paper we address, from a purely numerical point of view, the
question, raised in [20, 21], and partly considered in [22, 9, 3], whether a
certain function, referred to as "Euler Integral", is a quasi-integral along
the trajectories of the three-body problem. Differently from our previous
investigations, here we focus on the region of the "unperturbed separatrix",
which turns to be complicated by a collision singularity. Concretely, we reduce
the Hamiltonian to two degrees of freedom and, after fixing some energy level,
we discuss in detail the resulting three-dimensional phase space around an
elliptic and an hyperbolic periodic orbit. After measuring the strength of
variation of the Euler Integral (which are in fact small), we detect the
existence of chaos closely to the unperturbed separatrix. The latter result is
obtained through a careful use of the machinery of covering relations,
developed in [13, 24, 23].

12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph