Higher Dimensional Systems

Abstract

As we have seen in section I.1, there are many situations in which a map $\mathbb{R}^{{\rm n}} \rightarrow \mathbb{R}^{{\rm n}}$ seems more appropriate than a map $\mathbb{R}^1 \rightarrow \mathbb{R}^1$. The purpose of this section is to illustrate how the features of one-dimensional maps described in I.6 generalize to higher dimensions. We have already seen in the previous section that the numerical results seem to indicate a persistence of the universal behavior for higher dimensional systems. While we refer for the theorems to Section III.4, we want to illustrate here the salient features of their hypotheses in two dimensions.