Characteristics of singular entities of simple cell mappings

The method of cell-to-cell mapping has the potential to be a very effective and general method of global analysis for strongly non-linear systems. However, simple cell mappings being integer mappings, most of the classical methods of analysis based upon continuity and differentiability of the mapping are no longer applicable and, therefore, new notions need be introduced. In [6] the concept of singular multiplets is introduced for the cell functions associated with the cell mappings. In this paper we study the characteristics of these singular entities by examining the mapping properties of the cells in the singular entities and in their neighborhoods. The key tool used in classifying the mapping properties is the limit set of the mapping process of a cell. The work represents a continuing effort to develop the method of cell-to-cell mapping as a tool of global analysis and to provide the method with a sound and appropriate structure.