ABSTRACT
In the final chapter of the book we study general scalar difference equations for which there may be no unique explicit or recursive forms globally and the existence of solutions is not guaranteed by direct iteration because the equations do not unfold to self-maps of a higher dimensional space. Such equations may be called implicit or nonrecursive. In spite of difficulties in obtaining information about the solutions of such equations, we discover that essential ideas and methods from Chapters 3-7 on decompositions (or factorizations) of equations and reductions of their orders can be extended to nonrecursive equations in many cases.
