Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density of the set of symbolic dynamics with all ergodic measures
  supported on periodic orbits   Let $K$ be the Cantor set. We prove that arbitrarily close to a homeomorphism
$T:K\rightarrow K$ there exists a homeomorphism $\widetilde T:K\rightarrow K$
such that the $\alpha$-limit and the $\omega$-limit of every orbit is a
periodic orbit. We also prove that arbitrarily close to an endomorphism
$T:K\rightarrow K$ there exists an endomorphism $\widetilde T:K\rightarrow K$
close to $T$ such that every orbit is finally periodic.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat