In physics and mathematics, a number of ideas are named after

Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...

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Euler–Poincaré characteristic In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space' ...

* Hilbert–Poincaré series *

Poincaré–Bendixson theorem In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere. Theorem Given a differentiable real dynamical system defined on an op ...

* Poincaré–Birkhoff theorem * Poincaré–Birkhoff–Witt theorem, usually known as the PBW theorem * Poincaré algebra ** K-Poincaré algebra ** Super-Poincaré algebra * Poincaré–Bjerknes circulation theorem * Poincaré complex *

Poincaré conjecture In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured b ...

, one of the

Millennium Prize Problems The Millennium Prize Problems are seven well-known complex mathematics, mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem ...

Generalized Poincaré conjecture In the mathematical area of topology, the generalized Poincaré conjecture is a statement that a manifold that is a homotopy sphere a sphere. More precisely, one fixes a category of manifolds: topological (Top), piecewise linear (PL), or differen ...

Poincaré disk model In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk t ...

, a model of

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or János Bolyai, Bolyai–Nikolai Lobachevsky, Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For a ...

Poincaré duality In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology (mathematics), homology and cohomology group (mathematics), groups of manifolds. It states that if ''M'' is an ''n''-dim ...

** Twisted Poincaré duality * Poincaré–Einstein synchronization * Poincaré expansion * Poincaré group, the group of isometries of

Minkowski spacetime In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a s ...

, named in honour of Henri Poincaré ** K-Poincaré group *

Poincaré half-plane model In non-Euclidean geometry, the Poincaré half-plane model is a way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specifically, each point in the hyperbolic plane is represented using a Euclidean point with co ...

, a model of two-dimensional

* Poincaré homology sphere * Poincaré–Hopf theorem * Poincaré inequality ** Poincaré–Wirtinger inequality * Poincaré–Lelong equation *

Poincaré lemma In mathematics, the Poincaré lemma gives a sufficient condition for a closed differential form to be exact (while an exact form is necessarily closed). Precisely, it states that every closed ''p''-form on an open ball in R''n'' is exact for ''p'' ...

* Poincaré-Lefschetz duality *

Poincaré–Lindstedt method In perturbation theory, the Poincaré–Lindstedt method or Lindstedt–Poincaré method is a technique for uniformly approximating periodic solutions to ordinary differential equations, when regular perturbation approaches fail. The method remove ...

* Poincaré line bundle *

Poincaré map In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensiona ...

* Poincaré metric * Poincaré–Miranda theorem * Poincaré–Neumann operator * Poincaré plot * Poincaré polynomial * Poincaré recurrence * Poincaré residue * Poincaré separation theorem * Poincaré series (modular form) * Poincaré space *

Poincaré sphere (optics) Unpolarized light is light with a random, time-varying polarization. Natural light, like most other common sources of visible light, is produced independently by a large number of atoms or molecules whose emissions are uncorrelated. Unpolarize ...

* Poincaré–Steklov operator * Poincaré symmetry * Poincaré wave

Other

* Annales Henri Poincaré *

Institut Henri Poincaré The Henri Poincaré Institute (or IHP for ''Institut Henri Poincaré'') is a mathematics research institute part of Sorbonne University, in association with the Centre national de la recherche scientifique (CNRS). It is located in the 5th arrondi ...

Henri Poincaré Prize The Henri Poincaré Prize is awarded every three years since 1997 for exceptional achievements in mathematical physics and foundational contributions leading to new developments in the field. It is named after the French mathematician Henri Poincar ...

* Henri Poincaré University * Poincaré and the Three-Body Problem *

Poincaré (crater) Poincaré is a large lunar impact basin that lies in the southern hemisphere on the far side of the Moon. Most of the formation has been heavily eroded by subsequent impacts, leaving a battered formation with only rugged remnants of the origi ...

* Poincaré Medal * Poincaré Seminars *

Books with the title "Henri Poincaré"

References

{{DEFAULTSORT:List of things named after Henri Poincare Poincare Henri Poincaré