On open problems concerning distributional chaos for triangular maps Original Research Article

We show that in the class TT of the triangular maps (x,y)↦(f(x),gx(y))(x,y)↦(f(x),gx(y)) of the square there is a map of type 2∞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 TT with zero topological entropy, and contribute to an old problem formulated by A.N. Sharkovsky.