Some remarks on the Abel equation in the unit disk

DOI10.1112/jlms/jdm013zbMath1138.30018OpenAlexW1991978923MaRDI QIDQ5308173

Christian Pommerenke, Manuel D. Contreras, Santiago Diaz-Madrigal

Publication date: 27 September 2007

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/jlms/jdm013

zbMATH Keywords

Denjoy-Wolff pointintertwining mapparabolic pointiteration of analytic functions

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Functional equations for complex functions (39B32)

Related Items (20)

Commuting finite Blaschke products with no fixed points in the unit disk ⋮ Backward iteration in the unit ball ⋮ On the uniqueness of classical semiconjugations for self-maps of the disk ⋮ Loewner chains in the unit disk ⋮ Semigroups of composition operators on Hardy spaces of Dirichlet series ⋮ Uniqueness of holomorphic Abel functions at a complex fixed point pair ⋮ On Ulam stability of the inhomogeneous version of the general linear functional equation ⋮ Boundary behavior of the iterates of a self-map of the unit disk ⋮ Hypercyclic composition operators on spaces of real analytic functions ⋮ On the rate of convergence of semigroups of holomorphic functions at the Denjoy-Wolff point ⋮ Geometric description of the classification of holomorphic semigroups ⋮ Canonical models for holomorphic iteration ⋮ Asymptotic behavior of orbits of holomorphic semigroups ⋮ The linear fractional model on the ball ⋮ Non-tangential limits and the slope of trajectories of holomorphic semigroups of the unit disc ⋮ Second angular derivatives and parabolic iteration in the unit disk ⋮ A characterization of orthogonal convergence in simply connected domains ⋮ Slope problem for trajectories of holomorphic semigroups in the unit disk ⋮ Abel's functional equation and eigenvalues of composition operators on spaces of real analytic functions ⋮ Semigroups versus evolution families in the Loewner theory

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