Digons and angular derivatives of analytic self-maps of the unit disk

DOI10.1080/17476930701349828zbMath1132.30005arXivmath/0701272OpenAlexW1981958350MaRDI QIDQ5423143

Alexander Vasil'ev, Santiago Diaz-Madrigal, Manuel D. Contreras

Publication date: 22 October 2007

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701272

zbMATH Keywords

fixed pointangular derivativeDenjoy-Wolff pointreduced modulussemigroup of analytic functionsDigon

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Extremal problems for conformal and quasiconformal mappings, other methods (30C75)

Related Items

Angular derivatives for holomorphic self-maps of the disk, Boundary distortion and the Schwarzian derivative of a univalent function in a circular annulus, Value regions of univalent self-maps with two boundary fixed points, Editorial. Dedication to Alexander Vasil'ev (1962--2016), Boundary distortion estimates for holomorphic maps, Производная Шварца и покрытие дуг пучка окружностей голоморфными функциями, The Schwarz Lemma: Rigidity and Dynamics

Cites Work

• Analytic flows on the unit disk: angular derivatives and boundary fixed points
• Inequalities for the Angular Derivative of an Analytic Function in the Unit Disk
• Inequalities for Fixed Points of Holomorphic Functions