Talk:Poincaré map

??
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

Poincare Space
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. 137.82.36.10 (talk) 02:27, 9 October 2008 (UTC)

Question
Should it be specified where U is open? —Preceding unsigned comment added by 216.36.87.189 (talk) 20:56, 28 November 2010 (UTC)

first return map
Hi. I'm looking for definition of " first return map". Is it related with Poincare map ? --Adam majewski (talk) 18:38, 25 October 2011 (UTC)

Ambiguity and rewording proposal
The current article text contains:

”the locus of the Moon when it passes through the plane perpendicular to the Earth's orbit and passing through the Sun and the Earth at perihelion is a Poincaré map.”

On first reading, I interpreted it as contending that the Moon passes through the Sun and the Moon, which seems impossible. Only on second reading, I presumed that “passing” may also grammatically refer to “the plane”.

If that is the intended meaning, I propose to remove ambiguity by rewording like this:

”the locus of the Moon when it passes through the plane that is perpendicular to the Earth's orbit and passes through the Sun and the Earth at perihelion is a Poincaré map.”

Any well-motivated objections?Redav (talk) 15:32, 27 December 2023 (UTC)