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
StatementLet 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 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
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
- In Branch: Complex Analysis, Lead sentence
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