Fixed points of commuting holomorphic mappings other than the Wolff point

DOI10.1090/S0002-9947-03-03170-2zbMath1045.30014MaRDI QIDQ4804226

Filippo Bracci

Publication date: 10 April 2003

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

zbMATH Keywords

fixed pointsSchwarz lemmacommuting mappingsWolff pointboundary repelling fixed point

Mathematics Subject Classification ID

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) Boundary value problems in the complex plane (30E25) Linear composition operators (47B33)

Related Items (12)

Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk ⋮ Commuting finite Blaschke products with no fixed points in the unit disk ⋮ The stable subset of a univalent self-map ⋮ Inequalities for angular derivatives and boundary interpolation ⋮ The horofunction boundary of a Gromov hyperbolic space ⋮ Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces ⋮ Wolff-Denjoy theorems in nonsmooth convex domains ⋮ Backward orbits and petals of semigroups of holomorphic self-maps of the unit disc ⋮ Canonical models for the forward and backward iteration of holomorphic maps ⋮ Backward orbits in the unit ball ⋮ Solving the Schröder equation at the boundary in several variables ⋮ The Schwarz Lemma: Rigidity and Dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Composition operators and classical function theory
• Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
• When do finite Blaschke products commute?
• Commuting Analytic Functions
• Inequalities for the Angular Derivative of an Analytic Function in the Unit Disk
• Iteration and the Solution of Functional Equations for Functions Analytic In the Unit Disk
• Common fixed points of commuting holomorphic maps in the unit ball of ℂⁿ
• Angular derivatives at boundary fixed points for self-maps of the disk
• Fixed Points of Commuting Holomorphic Maps Without Boundary Regularity
• On Fixed Points of Commuting Analytic Functions
• Commuting Analytic Functions Without Fixed Points

This page was built for publication: Fixed points of commuting holomorphic mappings other than the Wolff point