In this extensive work, the authors give a complete self-contained
exposition on the subject of classic function theory and the most
recent developments in transcendental iteration. They clearly
present the theory of iteration of transcendental functions and
their analytic and geometric aspects. Attention is concentrated for
the first time on the dynamics of transcendental functions to
compliment the growing body of work on rational functions. The
subjects covered in detail include the fixed point theory, basic
properties of Fatou and Julia sets, components of Fatou sets, the
geometry of Julia sets, and the Hausdorff dimension of the Julia
set.
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