Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shadowing and Expansivity in Sub-Spaces   We address various notions of shadowing and expansivity for continuous maps
restricted to a proper subset of their domain. We prove new equivalences of
shadowing and expansive properties, we demonstrate under what conditions
certain expanding maps have shadowing, and generalize some known results in
this area. We also investigate the impact of our theory on maps of the
interval, in which context some of our results can be extended.

15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph