See Also: Poincare(dictionary)
Poincare, Raymond(encyclopedia)
Poincare, Henri(dictionary)
Poincare, (Jules-) Henri(encyclopedia)
Henri Poincare University Hospital(health)

Poincare (iou)



Poincare noun. M20.
[Jules-Henri Poincare (1854-1912), French mathematician and physicist.]
Math. & Physics. Used attrib. and in possess. to designate various concepts introduced by Poincare or arising out of his work.
Poincare conjecture = Poincare's conjecture below. Poincare cycle (a single circuit of) a simple closed curve in the phase space of a system, representing one possible solution of the governing differential equations. Poincare map, Poincare mapping (a) a representation of the phase space of a dynamic system, indicating all possible trajectories; (b) = Poincare section below. Poincare's conjecture: that any simply connected compact three-dimensional manifold is topologically equivalent to a sphere. Poincare section the intersection of a Poincare map (in sense (a)) with a given line, plane, etc.