Iteration of a class of multi-plateau mappings

Iteration is one of the most important topics in the field of functional equations, which is also concerned with dynamical systems and operator theory. In this paper we discuss a class of multi-plateau mappings with finitely many P-intervals whose range crosses the diagonals and classifies them into four classes. For each class the properties of all the orbits of the two endpoints of the P-intervals are investigated in a similar way as for symbolic dynamical systems, and finally the iteration of these multi-plateau mappings are given.