title: Poincaré theorem
text: # Poincaré theorem
  
  Poincaré theorem may refer to:
  
  * Poincaré conjecture, on homeomorphisms to the sphere;
  * Poincaré recurrence theorem, on sufficient conditions for recurrence to take place in dynamical systems;
  * Poincaré-Bendixson theorem, on the existence of attractors for two-dimensional dynamical systems;
  * Poincaré–Birkhoff–Witt theorem, concerning lie algebras and their universal envelopes;
  * Poincaré lemma.
  