Singular entities and an index theory for cell functions (Q799284)

Let \(Z^ n\) denote the set of \(n\)-tuples of integers. A mapping from \(Z^ n\) into \(Z^ n\) is called a cell mapping. A theory for such mappings was introduced and applied to global analysis of nonlinear systems in some recent papers [cf. the first author, J. Appl. Mech. 47, 931--939 (1980; Zbl 0452.58019); the first author and \textit{R. S. Gutallu}, ibid. 47, 940--948 (1980; Zbl 0452.58020)]. In the present paper, the authors continue to develop the theory by introducing the concepts of singular cells, singular doublets, etc. and presenting an index theory for one and two-dimensional cell mappings. It is hoped that through these and other developments, a coherent structure can be built up for the theory of cell mapping.