Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On decomposition of ambient surfaces admitting A-diffeomorphisms with
  nontrivial attractors and repellers   It is well-known that there is a close relationship between the dynamics of
diffeomorphisms satisfying the axiom $A$ and the topology of the ambient
manifold. In the given article, this statement is considered for the class
$\mathbb G(M^2)$ of $A$-diffeomorphisms of closed orientable surfaces such that
their non-wandering set consists of $k_f\geq 2$ connected components of
one-dimensional basic sets (attractors and repellers). We prove that the
ambient surface of every diffeomorphism $f\in \mathbb G(M^2)$ is homeomorphic
to the connected sum of $k_f$ closed orientable surfaces and $l_f$
two-dimensional tori such that the genus of each surface is determined by the
dynamical properties of appropriating connected component of a basic set and
$l_f$ is determined by the number and position of bunches, belonging to all
connected components of basic sets. We also prove that every diffeomorphism
from the class $\mathbb G(M^2)$ is $\Omega$-stable but is not structurally
stable.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex