# 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

**Wikidata**: [Q3527140](https://www.wikidata.org/wiki/Q3527140)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Poincaré–Birkhoff_theorem)  
**Source**: https://4ort.xyz/entity/poincar-birkhoff-theorem