Backward iteration in the unit ball

zbMath1269.30032arXiv0910.5451MaRDI QIDQ358943

Olena Ostapyuk

Publication date: 9 August 2013

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.5451

zbMATH Keywords

ellipticiterationhyperbolicanalytic mapunit ballbackward iterationboundary repelling fixed pointsintertwining map

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Boundary behavior of holomorphic functions of several complex variables (32A40) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)

Related Items (9)

Simultaneous models for commuting holomorphic self-maps of the ball ⋮ Corrigendum to: ``Backward iteration in strongly convex domains ⋮ The stable subset of a univalent self-map ⋮ The horofunction boundary of a Gromov hyperbolic space ⋮ Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces ⋮ Iteration in the disk and the ball: a survey of the role of hyperbolic geometry ⋮ Canonical models for the forward and backward iteration of holomorphic maps ⋮ Canonical models on strongly convex domains via the squeezing function ⋮ Backward orbits in the unit ball

Cites Work

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• Iterates of holomorphic self-maps of the unit ball in \(C^ n\)
• On the uniqueness of classical semiconjugations for self-maps of the disk
• Valiron's construction in higher dimension
• Valiron's theorem in the unit ball and spectra of composition operators
• The linear fractional model on the ball
• Norm convergence of normalized iterates and the growth of Kœnigs maps
• Schroeder's equation in several variables.
• Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
• Solving the Schröder equation at the boundary in several variables
• Quelques propriétés des applications analytiques d'une boule à \(m\) dimensions dans elle-même
• Local Contractions and a Theorem of Poincare
• On the Iteration of Analytic Functions in a Halplane II
• 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
• On the Iteration of Analytic Functions in a Halfplane, I
• Some remarks on the Abel equation in the unit disk

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