Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homoclinic classes with shadowing property   We show that for $C^1$ generic diffeomorphisms, an isolated homoclinic class
is shadowable if and only if homoclinic class is hyperbolic basic set.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga