Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ultragraph shift spaces and chaos   Motivated by C*-algebra theory, ultragraph edge shift spaces generalize
shifts of finite type to the infinite alphabet case. In this paper we study
several notions of chaos for ultragraph shift spaces. More specifically, we
show that Li-Yorke, Devaney and distributional chaos are equivalent conditions
for ultragraph shift spaces, and characterize this condition in terms of a
combinatorial property of the underlying ultragraph. Furthermore, we prove that
such properties imply the existence of a compact, perfect set which is
distributionally scrambled of type 1 in the ultragraph shift space (a result
that is not known for a labelled edge shift (with the product topology) of an
infinite graph).

8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs