ABSTRACT
This chapter introduces a geometric procedure that will help to understand the dynamics of one-dimensional maps. This procedure, called graphical analysis, enables to use the graph of a function to determine the behavior of orbits in many cases. Graphical analysis sometimes allows to describe the behavior of all orbits of a dynamical system. One should emphasize that graphical analysis is by no means a completely rigorous tool; in most cases one cannot use graphical analysis as a proof that certain dynamical phenomena occur. However, there is no question that this procedure is a valuable tool that helps explain what is going on. One succinct method for depicting all orbits of a dynamical system is the phase portrait of the system. This is a picture on the real line of the orbits. In the one-dimensional case, the phase portrait gives no more information than graphical analysis.
