Publication year: 2020
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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 Carathéodory prime ends topology and Gromov hyperbolicity theory.
Subject: Mathematics and Statistics, Functions of a Complex Variable, Dynamical Systems and Ergodic Theory, Functional Analysis, Ordinary Differential Equations, Geometry, Semigroups of holomorphic functions, Univalent functions, Hyperbolic metric, Iteration theory, Holomorphic ODE