Intro; Contents; Preface; Chapter 1 Semigroups of Linear Operators; 1.1 Linear operators. Spectrum and resolvent; 1.2 Continuous semigroups and their generators; 1.3 Numerical range of linear operators; 1.4 Analytic semigroups; 1.5 Cesàro and Abel averages of linear operators; 1.6 Abel averages: recent results; Chapter 2 Numerical Range; 2.1 Holomorphic mappings in Banach spaces; 2.2 Spectrum and resolvent of holomorphic mappings; 2.3 Numerical range; 2.4 Real part estimates; 2.5 Holomorphically dissipative and accretive mappings; 2.6 Growth estimates for the numerical range

2.7 Filtration of dissipative mappingsChapter 3 Fixed Points of Holomorphic Mappings; 3.1 Fixed points in the unit disk; 3.2 Fixed points in the Hilbert ball; 3.3 Boundary fixed points and the horosphere function; 3.4 Canonical representation of the fixed point set; 3.5 Around the Earle-Hamilton fixed point theorem; 3.6 Inexact orbits of holomorphic mappings; 3.7 The Bohl-Poincaré-Krasnoselskii Theorem; 3.8 Fixed points of pseudo-contractive holomorphic mappings; Chapter 4 Semigroups of Holomorphic Mappings; 4.1 Generated semigroups; 4.2 Stationary points of semigroups

4.3 Flow invariance conditions4.4 Semi-complete vector fields on bounded symmetric domains; 4.5 Rates of convergence of semigroups; 4.6 Semigroups and pseudo-contractive holomorphic mappings; 4.7 Semigroups on the Hilbert ball; Chapter 5 Ergodic Theory of Holomorphic Mappings; 5.1 General remarks; 5.2 Power bounded holomorphic mappings; 5.3 Ergodicity and fixed points; 5.4 Numerical range and power boundedness; 5.5 Dissipative and pseudo-contractive mappings; 5.6 Examples; Chapter 6 Some Applications; 6.1 Bloch radii; 6.2 Radii of starlikeness and spirallikeness

6.3 Analytic extension of one-parameter semigroups6.4 Analytic extension of semigroups without stationary points; 6.5 Composition operators and semigroups; 6.6 Analytic semigroups of composition operators; 6.7 Semigroups of composition operators on Hp(II); Bibliography; Subject Index; Author Index