On the rate of convergence of semigroups of holomorphic functions at the Denjoy-Wolff point

DOI10.4171/rmi/1179zbMath1467.30007OpenAlexW3005726971MaRDI QIDQ1998677

Dimitrios Betsakos, Manuel D. Contreras, Santiago Diaz-Madrigal

Publication date: 7 March 2021

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rmi/1179

zbMATH Keywords

harmonic measureDenjoy-Wolff pointsemigroups of holomorphic functions

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics induced by flows and semiflows (37C10)

Related Items (8)

Asymptotic monotonicity of the orthogonal speed and rate of convergence for semigroups of holomorphic self-maps of the unit disc ⋮ Semigroups of Composition Operators on Vector-Valued Hardy Spaces ⋮ Boundary fixed points vs. critical points in semigroups of holomorphic self-maps of the unit disc ⋮ Path-lifting properties of the exponential map with applications to geodesics ⋮ Conformal invariants and the angular derivative problem ⋮ Speeds of convergence of orbits of non-elliptic semigroups of holomorphic self-maps of the unit disk ⋮ Asymptotic upper bound for tangential speed of parabolic semigroups of holomorphic self-maps in the unit disc ⋮ Angular derivatives and semigroups of holomorphic functions

Cites Work

• Angular and unrestricted limits of one-parameter semigroups in the unit disk
• Convergence characteristics of one-parameter continuous semigroups
• On the rate of convergence of parabolic semigroups of holomorphic functions
• Linearization models for complex dynamical systems. Topics in univalent functions, functional equations and semigroup theory.
• Semigroups of analytic functions and composition operators
• Extremal length and univalent functions. I: The angular derivative
• Composition operators and classical function theory
• Analytic flows on the unit disk: angular derivatives and boundary fixed points
• Kœnigs-type linearization models and asymptotic behavior of one-parameter semigroups
• Canonical models for holomorphic iteration
• Iteration and the Solution of Functional Equations for Functions Analytic In the Unit Disk
• On the Iteration of Analytic Functions in a Halfplane, I
• Non-tangential limits and the slope of trajectories of holomorphic semigroups of the unit disc
• The Schwarz Lemma: Rigidity and Dynamics
• Some remarks on the Abel equation in the unit disk
• On boundary critical points for semigroups of analytic functions
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