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 .
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