On open problems concerning distributional chaos for triangular maps

We show that in the class T of the triangular maps (x,y)?(f(x),g_x(y)) of the square there is a map of type 2^∞ with non-minimal recurrent points which is not DC3. We also show that every DC1 continuous map of a compact metric space has a trajectory which cannot be (weakly) approximated by trajectories of compact periodic sets. These two results make possible to answer some open questions concerning classification of maps in T with zero topological entropy, and contribute to an old problem formulated by A.N. Sharkovsky.