Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Action of Non Abelian Group Generated by Affine Homotheties on R^n   In this paper, we study the action of non abelian group G generated by affine
homotheties on R^n. We prove that G satisfies one of the following properties:
(i) there exist a subgroup F_{G} of R\{0} containing 0 in its closure, a
G-invariant affine subspace E_{G} of R^n and a in E_{G} such that for every x
in R^n the closure of the orbit G(x) is equal to F_{G} .(x - a) +E_{G}. In
particular, G(x) is dense in E_{G} for every x in E_{G} and every orbit of U =
R^n\E_{G} is minimal in U. (ii) there exists a closed subgroup H_{G} of R^n and
a in R^n such that for every x in R^n, the closure of the orbit G(x) is equal
to the union of (x + H_{G}) and (-x + a + H_{G}).

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat