As before, in order to obtain chaos for a map the equations (6)
must contain at least one nonlinear term. However, * for a map chaos can
arise even for a one-dimensional system* [3],
which should be contrasted with the
corresponding criterion for a flow. This is a very important point since,
in order to study chaotic effects one need only consider one- or
two-dimensional maps, whereas for a flow at least three dimensions is
mandatory. Moreover, for a given dimensionality **n**, the map equations
(6) are much easier to use than the flow equations (3).
For a mapping, we study the dynamics by simply iterating, whereas for a
flow we must solve a system of differential equations, which in general is
nontrivial.
Thus, for the remainder of this chapter we will focus on chaos in several
simple one- and two-dimensional maps.