Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new version of distributional chaos and the relations between
  distributional chaos in a sequence and other concepts of chaos   In this paper we consider relations between distributional chaos in a
sequence with distributional chaos, w-chaos, R-T chaos, DC 3, respectively). We
give a sufficient condition and prove that the distributional chaos is
equivalent to the distributional chaos in a sequence under this condition.
Besides, we get that distributional chaos in a sequence and w-chaos(R-T chaos,
DC 3, respectively)do not imply each other. Finally, we give a new definition
of chaos, named DC 2', which is similar to DC 2, and show that for any integer
N > 0, f is DC 2' if and only if f^N is also DC 2'.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph