Valiron's construction in higher dimension

DOI10.4171/RMI/593zbMath1198.32006arXiv0710.2020OpenAlexW1993872450MaRDI QIDQ971956

Filippo Bracci, Graziano Gentili, Pietro Poggi-Corradini

Publication date: 17 May 2010

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

Full work available at URL: https://arxiv.org/abs/0710.2020

zbMATH Keywords

linearizationholomorphic dynamicssemiconjugationintertwining maps

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Other generalizations of function theory of one complex variable (32A30) Holomorphic functions of several complex variables (32A10)

Related Items (9)

Abstract Basins of Attraction ⋮ Backward iteration in the unit ball ⋮ Simultaneous models for commuting holomorphic self-maps of the ball ⋮ Iteration in the disk and the ball: a survey of the role of hyperbolic geometry ⋮ Valiron's theorem in the unit ball and spectra of composition operators ⋮ Canonical models for the forward and backward iteration of holomorphic maps ⋮ Canonical models on strongly convex domains via the squeezing function ⋮ Canonical models for holomorphic iteration ⋮ Backward orbits in the unit ball

Cites Work

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• Iterates of holomorphic self-maps of the unit ball in \(C^ n\)
• The linear fractional model on the ball
• On holomorphic maps which commute with hyperbolic automorphisms
• Solving the Schröder equation at the boundary in several variables
• Cyclic phenomena for composition operators
• Iteration and the Solution of Functional Equations for Functions Analytic In the Unit Disk
• On Asymptotic Iteration of Analytic Functions in the Disk
• On the Iteration of Analytic Functions in a Halfplane, I
• Several Complex Variables and the Geometry of Real Hypersurfaces

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