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Koenigs function

In mathematics, the Koenigs function is a function arising in complex analysis and dynamical systems. Introduced in 1884 by the French mathematician Gabriel Koenigs, it gives a canonical representation as dilations of a univalent holomorphic mapping, or a semigroup of mappings, of the unit disk in the complex numbers into itself.

Measurement, Existence and uniqueness of Koenigs function & Koenigs function of a semigroup

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Existence and uniqueness of Koenigs function

Holomorphic functionMöbius transformationDenjoy-Wolff theoremKoenigs (1884)Schröder's equation
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Koenigs function of a semigroup

Iterated function
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Structure of univalent semigroups

Starlike
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Overview

MathematicsComplex analysisDynamical systemsGabriel KoenigsUnivalent holomorphic mapping
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Existence and uniqueness of Koenigs function

Koenigs function of a semigroup

Structure of univalent semigroups

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Koenigs function

Nodes26
Edges25
Triples1
Avg. degree1.92
Density0.076923
Components1

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Koenigs function

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Koenigs function → function arising in complex analysis and dynamical systems

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Important terminology

function koenigs univalent semigroup holomorphic complex isbn displaystyle mathematics lambda fs 1884 mapping disk semigroups defined equation hence theory dynamical

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Koenigs functionis afunction arising in complex analysis and dynamical systems0.90text

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