Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sensitivity, local stable/unstable sets and shadowing   In this paper we study local stable/unstable sets of sensitive homeomorphisms
with the shadowing property defined on compact metric spaces. We prove that
local stable/unstable sets always contain a compact and perfect subset of the
space. As a corollary we generalize results in [6] and [11] proving that
positively countably expansive homeomorphisms defined on compact metric spaces
satisfying either transitivity and the shadowing property, or the L-shadowing
property, can only be defined in countably spaces.

1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat