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
Press Enter · cited answer in seconds

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 October 13, 2026, from https://4ort.xyz/entity/poincar-birkhoff-theorem
MLA “Poincaré–Birkhoff theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 13 Oct. 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: 2026-10-13}}
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 2026-10-13)

Canonical URL: https://4ort.xyz/entity/poincar-birkhoff-theorem · Last refreshed:

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. 13w 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"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.