Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the regularization of the collision solutions of the one-center
  problem with weak forces   We study the possible regularization of collision solutions for one centre
problems with a weak singularity. In the case of logarithmic singularities, we
consider the method of regularization via smoothing of the potential. With this
technique, we prove that the extended flow, where collision solutions are
replaced with a transmission trajectory, is continuous, though not
differentiable, with respect to the initial data.

33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci