Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the weakest version of distributional chaos   The aim of the paper is to correct and improve some results concerning
distributional chaos of type 3. We show that in a general compact metric space,
distributional chaos of type 3, denoted DC3, even when assuming the existence
of an uncountable scrambled set, is a very weak form of chaos. In particular,
(i) the chaos can be unstable (it can be destroyed by conjugacy), and (ii) such
an unstable system may contain no Li-Yorke pair. However, the definition can be
strengthened to get DC$2\frac{1}{2}$ which is a topological invariant and
implies Li-Yorke chaos, similarly as types DC1 and DC2; but unlike them, strict
DC$2\frac{1}{2}$ systems must have zero topological entropy.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int