This is a one-stop introduction to the methods of ergodic theory
applied to holomorphic iteration. The authors begin with
introductory chapters presenting the necessary tools from ergodic
theory thermodynamical formalism, and then focus on recent
developments in the field of 1-dimensional holomorphic iterations
and underlying fractal sets, from the point of view of geometric
measure theory and rigidity. Detailed proofs are included.
Developed from university courses taught by the authors, this book
is ideal for graduate students. Researchers will also find it a
valuable source of reference to a large and rapidly expanding
field. It eases the reader into the subject and provides a vital
springboard for those beginning their own research. Many helpful
exercises are also included to aid understanding of the material
presented and the authors provide links to further reading and
related areas of research.
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