Theorem

Denjoy-Wolff Theorem

Analysis

The Denjoy-Wolff Theorem, a result in complex analysis and dynamical systems, concerns the fixed points and iteration behavior of holomorphic mappings of the open unit disc in the complex numbers into itself. It was proved independently in 1926 by the French mathematician Arnaud Denjoy and the Dutch mathematician Julius Wolff.

Facts

Statement

Let D be the open unit disk in the complex numbers and f a holomorphic function mapping D into D that is not an automorphism of D. Then there is a unique point z in the closure of D such that the iterates of f tend to z uniformly on compact subsets of D. 1

Proof Year

1926 1

Classification

Statement Form

Existence Theorem 1

Statement Form

Uniqueness Theorem 1

Connections

Has Statement Form

Existence Theorem

Uniqueness Theorem

In Branch

Complex Analysis

Source Denjoy-Wolff theorem (Wikipedia)

Principal Result Of

Arnaud Denjoy

Source Denjoy-Wolff theorem (Wikipedia)

Proved By

Arnaud Denjoy

Source Denjoy-Wolff theorem (Wikipedia)

Sources

1. Denjoy-Wolff theorem (Wikipedia)

Statement
Then there is a unique point z in the closure of D such that the iterates of f tend to z uniformly on compact subsets of D
Introduction
proved independently in 1926
Proved By: Arnaud Denjoy, Lead sentence
The result was proved independently in 1926 by the French mathematician Arnaud Denjoy and the Dutch mathematician Julius Wolff.
Principal Result Of: Arnaud Denjoy, Lead sentence of the article on the result
The result was proved independently in 1926 by the French mathematician Arnaud Denjoy and the Dutch mathematician Julius Wolff.
In Branch: Complex Analysis, Lead sentence

Denjoy-Wolff Theorem

Has Statement Form

In Branch

Principal Result Of

Proved By

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