Examples of Global Analysis by Simple Cell Mapping

Abstract

In the last five chapters the simple cell mappings are studied in their own right as transformations of an N-tuple of integers to an N-tuple of integers. In this chapter we use simple cell mappings as tools to investigate the global behavior of dynamical systems governed by point mappings and differential equations. We first review the center point method by which a simple cell mapping can be constructed for a point mapping or for an ordinary differential equation governing the system. Next, we discuss a special technique called compactification which allows us to construct a simple cell mapping over a finite set of cells S without introducing the concept of sink cell.