In symplectic topology and dynamical systems, PoincarĂ©âBirkhoff theorem (also known as PoincarĂ©âBirkhoff fixed point theorem and PoincarĂ©'s last geometric theorem) states that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points.
The PoincarĂ©âBirkhoff theorem was discovered by Henri PoincarĂ©, who published it in a 1912 paper titled "Sur un thĂ©orĂšme de gĂ©omĂ©trie", and proved it for some special cases. The general case was proved by George D. Birkhoff in his 1913 paper titled "Proof of PoincarĂ©'s geometric theorem". [1] [2]
In symplectic topology and dynamical systems, PoincarĂ©âBirkhoff theorem (also known as PoincarĂ©âBirkhoff fixed point theorem and PoincarĂ©'s last geometric theorem) states that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points.
The PoincarĂ©âBirkhoff theorem was discovered by Henri PoincarĂ©, who published it in a 1912 paper titled "Sur un thĂ©orĂšme de gĂ©omĂ©trie", and proved it for some special cases. The general case was proved by George D. Birkhoff in his 1913 paper titled "Proof of PoincarĂ©'s geometric theorem". [1] [2]