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Don't we mean 'perihelion', not 'parhelion'? mat_x 07:47, 4 Aug 2004 (UTC)
changed "hyperplane" to "hypersurface" because it needn't be a plane, and very seldom is in practice. Added transversal, because this is normally assumed, if not, then in some parts the hypersurface is invariant under the flow and your poincare map is identity in these parts - very useful.
Definition seems wrong: "P(p)=p"?
"...semi-orbit of x..."? why not y
I don't think that Poincare space should redirect to Poincare map. A Poincare space is any topological space that is subject to Poincare duality (eg, a compact manifold, a strong retract of a compact manifold, etc). A Poincare map seems to be in the realm of dynamical systems. 18.104.22.168 (talk) 02:27, 9 October 2008 (UTC)