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Continuous Semigroups of Holomorphic Self-maps of the Unit Disc (Hardcover, 1st ed. 2020)
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Continuous Semigroups of Holomorphic Self-maps of the Unit Disc (Hardcover, 1st ed. 2020)
Series: Springer Monographs in Mathematics
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The book faces the interplay among dynamical properties of
semigroups, analytical properties of infinitesimal generators and
geometrical properties of Koenigs functions. The book includes
precise descriptions of the behavior of trajectories, backward
orbits, petals and boundary behavior in general, aiming to give a
rather complete picture of all interesting phenomena that occur. In
order to fulfill this task, we choose to introduce a new point of
view, which is mainly based on the intrinsic dynamical aspects of
semigroups in relation with the hyperbolic distance and a deep use
of Caratheodory prime ends topology and Gromov hyperbolicity
theory. This work is intended both as a reference source for
researchers interested in the subject, and as an introductory book
for beginners with a (undergraduate) background in real and complex
analysis. For this purpose, the book is self-contained and all
non-standard (and, mostly, all standard) results are proved in
details.
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