Editing Henri Poincaré (section)

==See also==
===Concepts===
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* [[Hopf bifurcation|Poincaré–Andronov–Hopf bifurcation]]
* [[Poincaré complex]] – an abstraction of the singular chain complex of a closed, orientable manifold
* [[Poincaré duality]]
* [[Poincaré disk model]]
* [[Asymptotic expansion|Poincaré expansion]]
* [[Gauge fixing#Multipolar gauge|Poincaré gauge]]
* [[Poincaré group]]
* [[Poincaré half-plane model]]
* [[Homology sphere#Poincaré homology sphere|Poincaré homology sphere]]
* [[Poincaré inequality]]
* [[Closed and exact differential forms#Poincaré lemma|Poincaré lemma]]
* [[Poincaré map]]
* [[Poincaré residue]]
* [[Poincaré series (modular form)]]
* [[Poincaré space]]
* [[Poincaré metric]]
* [[Poincaré plot]]
* [[Betti number#Poincaré polynomial|Poincaré polynomial]]
* [[Hilbert–Poincaré series|Poincaré series]]
* [[Poincaré sphere (optics)|Poincaré sphere]]
* [[Einstein synchronisation|Poincaré–Einstein synchronisation]]
* [[Poincaré–Lelong equation]]
* [[Poincaré–Lindstedt method]]
* [[Poincaré–Lindstedt perturbation theory]]
* [[Poincaré–Steklov operator]]
* [[Euler characteristic|Euler–Poincaré characteristic]]
* [[Neumann–Poincaré operator]]
* [[Reflecting Function]]
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===Theorems===
Here is a list of theorems proved by Poincaré:
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* [[Poincaré's recurrence theorem]]: certain systems will, after a sufficiently long but finite time, return to a state very close to the initial state.
* [[Poincaré–Bendixson theorem]]: a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.
* [[Poincaré–Hopf theorem]]: a generalization of the hairy-ball theorem, which states that there is no smooth vector field on a sphere having no sources or sinks.
* [[Poincaré–Lefschetz duality theorem]]: a version of Poincaré duality in geometric topology, applying to a manifold with boundary
* [[Poincaré separation theorem]]: gives the upper and lower bounds of eigenvalues of a real symmetric matrix B'AB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B.
* [[Poincaré–Birkhoff theorem]]: every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points.
* [[Poincaré–Birkhoff–Witt theorem]]: an explicit description of the universal enveloping algebra of a Lie algebra.
* [[Kelvin's circulation theorem#Poincaré–Bjerknes circulation theorem|Poincaré–Bjerknes circulation theorem]]:  theorem about a conservation of quantity for the rotating frame.
* [[Poincaré conjecture]] (now a theorem): Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
* [[Poincaré–Miranda theorem]]: a generalization of the [[intermediate value theorem]] to ''n'' dimensions.
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=== Other ===
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*[[French epistemology]]
*[[History of special relativity]]
*[[List of things named after Henri Poincaré]]
*[[Institut Henri Poincaré]], Paris
*[[Brouwer fixed-point theorem]]
*[[Relativity priority dispute]]
*[[Epistemic structural realism]]<ref>[http://plato.stanford.edu/entries/structural-realism/#Rel "Structural Realism"]: entry by James Ladyman in the ''[[Stanford Encyclopedia of Philosophy]]''</ref>
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