Poincaré–Birkhoff theorem

in symplectic topology, the theorem that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points
Thing fixed_point_theorem Q3527140
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Poincaré–Birkhoff theorem

Summary

Poincaré–Birkhoff theorem is a fixed-point theorem[1]. It draws 71 Wikipedia views per month (fixed_point_theorem category, ranking #8 of 14).[2]

Key Facts

  • Poincaré–Birkhoff theorem is credited with the discovery of Henri Poincaré[3].
  • Poincaré–Birkhoff theorem's instance of is recorded as fixed-point theorem[4].
  • Poincaré–Birkhoff theorem's instance of is recorded as theorem[5].
  • Henri Poincaré is named after Poincaré–Birkhoff theorem[6].
  • George David Birkhoff is named after Poincaré–Birkhoff theorem[7].
  • Poincaré–Birkhoff theorem's time of discovery or invention is recorded as 1912[8].
  • Poincaré–Birkhoff theorem's maintained by WikiProject is recorded as WikiProject Mathematics[9].

Body

Definition and Type

Recorded instance of include fixed-point theorem[4] and theorem[5].

Origins

Things named after include Henri Poincaré[6], a mathematician[10], 1854–1912[11], of France[12], awarded the Poncelet Prize[13], specialised in algebraic geometry[14] and George David Birkhoff[7], a mathematician[15], 1884–1944[16], of United States[17], awarded the Bôcher Memorial Prize[18], specialised in topology[19].

Why It Matters

Poincaré–Birkhoff theorem draws 71 Wikipedia views per month (fixed_point_theorem category, ranking #8 of 14).[2] It has Wikipedia articles in 6 language editions, a strong signal of global cultural recognition.[20] It is known by 4 alternative names across languages and contexts.[21]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [4] . wikidata.org.
  2. [5] . wikidata.org.
  3. [3] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.

Inline context (facts about related entities)

  1. [10] . Wikidata. wikidata.org. → on this site
  2. [11] . Wikidata. wikidata.org. → on this site
  3. [12] . Wikidata. wikidata.org. → on this site
  4. [13] . Wikidata. wikidata.org. → on this site
  5. [14] . Wikidata. wikidata.org. → on this site
  6. [15] . Wikidata. wikidata.org. → on this site
  7. [16] . Wikidata. wikidata.org. → on this site
  8. [17] . Wikidata. wikidata.org. → on this site
  9. [18] . Wikidata. wikidata.org. → on this site
  10. [19] . Wikidata. wikidata.org. → on this site

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [20] . Wikidata sitelinks. wikidata.org.
  3. [21] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Poincaré–Birkhoff theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/poincar-birkhoff-theorem
MLA “Poincaré–Birkhoff theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/poincar-birkhoff-theorem.
BibTeX @misc{4ortxyz_poincar-birkhoff-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Poincaré–Birkhoff theorem}}, year = {2026}, url = {https://4ort.xyz/entity/poincar-birkhoff-theorem}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Poincaré–Birkhoff theorem — https://4ort.xyz/entity/poincar-birkhoff-theorem (retrieved 2026-05-03)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 6d ago · Nyuhn · 2026-07-10 view diff on Wikidata ↗
    P14541 4FqZYR
    Aliases
    Named after
    Instance of fixed-point theorem, theorem
    + 4 other properties edited (see Wikidata diff for full list)
    "/* wbeditentity-update:0| */ QuickStatements 3.0 [[:toollabs:qs-dev/batch/40849|batch #40849]]: ZGBK ID"
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