Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonintegrability and Chaos in the Anisotropic Manev Problem   The anisotropic Manev problem, which lies at the intersection of classical,
quantum, and relativity physics, describes the motion of two point masses in an
anisotropic space under the influence of a Newtonian force-law with a
relativistic correction term. Using an extension of the Poincare'-Melnikov
method, we first prove that for weak anisotropy, chaos shows up on the
zero-energy manifold. Then we put into the evidence a class of isolated
periodic orbits and show that the system is nonintegrable. Finally, using the
geodesic deviation approach, we prove the existence of a large non-chaotic set
of uniformly bounded and collisionless solutions.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph