Iterations of continuous maps of an interval to itself serve as the
simplest examples of models for dynamical systems. These models present
an interesting mathematical structure going far beyond the simple
equilibrium solutions one might expect. If, in addition, the dynamical
system depends on an experimentally controllable parameter, there is a
corresponding mathematical structure revealing a great deal about
interrelations between the behavior for different parameter values.
This work explains some of the early results of this theory to
mathematicians and theoretical physicists, with the additional hope of
stimulating experimentalists to look for more of these general phenomena
of beautiful regularity, which oftentimes seem to appear near the much
less understood chaotic systems. Although continuous maps of an interval
to itself seem to have been first introduced to model biological
systems, they can be found as models in most natural sciences as well as
economics.
Iterated Maps on the Interval as Dynamical Systems is a classic
reference used widely by researchers and graduate students in
mathematics and physics, opening up some new perspectives on the study
of dynamical systems .