On new chaotic mappings in symbol space

A well known chaotic mapping in symbol space is a shift mapping. However, other chaotic mappings in symbol space exist too. The basic change is to consider the process not only at a set of times which are equally spaced, say at unit time apart (a shift mapping), but at a set of times which are not equally spaced, say if the unit time can not be fixed. The increasing mapping as a generalization of the shift mapping and the k-switchmapping are introduced. The increasing and k-switch mappings are chaotic.