  In discrete dynamical system $(X, f)$ where $X$ is a topological space and $f
\in C(X,X)$, three notions of distributional chaos were defined. They were
denoted by $DC1, DC2$ and $DC3$. For interval systems such three notions
coincide and they will be denoted by DC-chaos. Generally speaking we have $DC1
\subseteq DC2 \subseteq DC3$-chaos.
  We wonder if it is possible that chaos can concentrate in some points and
develop a local idea of the distributional chaos. Answering to this question,
in [12] is introduced the new notion of $DCi$-points for $i = 1,2,3$. Such
special points are those in which DC-chaos of different types concentrate. Also
in [12] it is proved that if $f$ is continuous interval map with positive
topological entropy, then there is at least one DC1-point in the system.
  In this paper it is proved that in the symbolic space $(\Sigma, \sigma) $
where $\sigma$ is the shift map, every point of $\Sigma$ is a DC1-point. This
result is necessary to prove one of the main results of the paper. If $h(f) > 0
$ for an interval system, then it has an uncountable set of DC1-points and
moreover the set can be chosen perfect.
  In greater dimensions than one, we deal with triangular systems on $I^{2}$.
In this case the relationship between topological entropy and different cases
of distributional chaos is not clearly understood and several different results
are possible. In the paper we use an example of $F$ given by Kolyada in [9] to
prove that the corresponding two dimensional system $(I^{2}, F)$ has positive
topological entropy but without containing DC2-points, proving that there is no
concentration of DC2-chaos
