Semi-groups of analytic maps

DOI10.1007/BF03320988zbMath1015.30010OpenAlexW2058867828MaRDI QIDQ1848428

Alan F. Beardon

Publication date: 2001

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03320988

zbMATH Keywords

Denjoy-Wolff theoremhyperbolic domaincomposition of analytic maps

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) Normal functions of one complex variable, normal families (30D45)

Related Items (3)

Generalized iteration ⋮ Semi-groups of analytic functions that contain the identity map ⋮ Stability of the Denjoy-Wolff theorem

Cites Work

• Compositions of contractions
• On compositions of analytic self-mappings of a convex domain
• Compositions of analytic functions of the form \(F_ n(z)=F_{n-1}(f_ n(z))\), \(f_ n(z)\to f(z)\)
• A generalization of a theorem of Beardon on analytic contraction mappings
• A convergence question inspired by Stieltjes and by value sets in continued fraction theory
• Towers of exponents and other composite maps
• Iteration of Contractions and Analytic Maps
• The dynamics of contractions
• Random iteration of analytic maps
• On the number of 1-1 directly conformal maps which a multiply-connected plane region of finite connectivity 𝑝({>2}) admits onto itself
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