Pointwise convergence on the boundary in the Denjoy-Wolff theorem

DOI10.1216/RMJ-2010-40-4-1275zbMath1210.30009arXivmath/0407133MaRDI QIDQ990320

Pietro Poggi-Corradini

Publication date: 7 September 2010

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407133

zbMATH Keywords

harmonic measureelliptic mappinginner functionanalytic self-mapDenjoy-Wolff theoremhyperbolic mappingconvergence on the boundaryiteration of analytic functionsparabolic mapping

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Capacity and harmonic measure in the complex plane (30C85)

Related Items (8)

Holomorphic semigroups of finite shift in the unit disc ⋮ Quantitative mixing results and inner functions ⋮ Boundary behavior of the iterates of a self-map of the unit disk ⋮ Angular and unrestricted limits of one-parameter semigroups in the unit disk ⋮ Geometric description of the classification of holomorphic semigroups ⋮ Dirichlet-to-Robin operators via composition semigroups ⋮ Second angular derivatives and parabolic iteration in the unit disk ⋮ The Linear Fractional Model Theorem and Aleksandrov-Clark measures

Cites Work

• Complex dynamics
• The Hardy class of Koenigs maps
• Norm convergence of normalized iterates and the growth of Kœnigs maps
• Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
• On convergence to the Denjoy-Wolff point
• On the Iteration of Analytic Functions in a Halfplane, I
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