Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nilpotent Centers in $\mathbb{R}^3$   Consider analytical three-dimensional differential systems having a singular
point at the origin such that its linear part is $y\partial_x-\lambda
z\partial_z$ for some $\lambda\neq 0$. The restriction of such systems to a
Center Manifold has a nilpotent singular point at the origin. We study the
formal integrability and the center problem for those types of singular points
in the monodromic case. Our approach do not require polynomial approximations
of the Center Manifold in order to study the center problem. As a byproduct, we
obtain some useful results for planar $C^r$ systems having a nilpotent
singularity. We conclude the work solving the Nilpotent Center Problem for the
Generalized Lorenz system and the Hide-Skeldon-Acheson dynamo system.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin