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

Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...

: *

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 In mathematics, and in particular in the field of algebra, a Hilbert–Poincaré series (also known under the name Hilbert series), named after David Hilbert and Henri Poincaré, is an adaptation of the notion of dimension to the context of grade ...

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 In symplectic topology and dynamical systems, Poincaré–Birkhoff theorem (also known as Poincaré–Birkhoff fixed point theorem and Poincaré's last geometric theorem) states that every area-preserving, orientation-preserving homeomorphism of a ...

Poincaré–Birkhoff–Witt theorem In mathematics, more specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a Lie algebra. It is named after Henri Poi ...

, usually known as the PBW theorem * Poincaré algebra ** K-Poincaré algebra **

Super-Poincaré algebra In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras (without central charges or internal symme ...

* Poincaré–Bjerknes circulation theorem *

Poincaré complex In mathematics, and especially topology, a Poincaré complex (named after the mathematician Henri Poincaré) is an abstraction of the singular chain complex of a closed, orientable manifold. The singular homology and cohomology groups of a close ...

Poincaré conjecture In the mathematics, mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the Characterization (mathematics), characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dim ...

, one of the

Millennium Prize Problems The Millennium Prize Problems are seven well-known complex 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. According ...

** Generalized Poincaré conjecture *

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 th ...

, a model of

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' ...

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

Twisted Poincaré duality In mathematics, the twisted Poincaré duality is a theorem removing the restriction on Poincaré duality to oriented manifolds. The existence of a global orientation is replaced by carrying along local information, by means of a local coefficient ...

* Poincaré–Einstein synchronization * Poincaré expansion *

Poincaré group The Poincaré group, named after Henri Poincaré (1906), was first defined by Hermann Minkowski (1908) as the group of Minkowski spacetime isometries. It is a ten-dimensional non-abelian Lie group that is of importance as a model in our und ...

, the group of isometries of

Minkowski spacetime In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inert ...

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

Poincaré half-plane model In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H = \, together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry. Equivalently the Poincaré ha ...

, a model of two-dimensional

* Poincaré homology sphere *

Poincaré–Hopf theorem In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used in differential topology. It is named after Henri Poincar ...

Poincaré inequality In mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry ...

** Poincaré–Wirtinger inequality * Poincaré–Lelong equation *

Poincaré lemma In mathematics, especially vector calculus and differential topology, a closed form is a differential form ''α'' whose exterior derivative is zero (), and an exact form is a differential form, ''α'', that is the exterior derivative of another diff ...

* 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 In mathematics, a dual abelian variety can be defined from an abelian variety ''A'', defined over a field ''K''. Definition To an abelian variety ''A'' over a field ''k'', one associates a dual abelian variety ''A''v (over the same field), which ...

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 In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry ...

Poincaré–Miranda theorem In mathematics, the Poincaré–Miranda theorem is a generalization of intermediate value theorem, from a single function in a single dimension, to functions in dimensions. It says as follows: ::Consider n continuous functions of n variables, f_ ...

* Poincaré–Neumann operator *

Poincaré plot A Poincaré plot, named after Henri Poincaré, is a type of recurrence plot used to quantify self-similarity in processes, usually periodic functions. It is also known as a return map. Poincaré plots can be used to distinguish chaos from random ...

Poincaré polynomial In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of ''n''-dimensional simplicial complexes. For the most reasonable finite-dimensional topological space, spaces (such as compact manifolds ...

Poincaré recurrence Poincaré is a French surname. Notable people with the surname include: * Henri Poincaré (1854–1912), French physicist, mathematician and philosopher of science * Henriette Poincaré (1858-1943), wife of Prime Minister Raymond Poincaré * Luci ...

Poincaré residue In mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory. It is just one of a number of such possible extensions. Given a hypersurface X ...

* Poincaré separation theorem *

Poincaré series (modular form) In number theory, a Poincaré series is a mathematical series generalizing the classical theta series that is associated to any discrete group of symmetries of a complex domain, possibly of several complex variables. In particular, they genera ...

Poincaré space In algebraic topology, a Poincaré space is an ''n''-dimensional topological space with a distinguished element ''µ'' of its ''n''th homology group such that taking the cap product with an element of the ''k''th cohomology group yields an isomorphi ...

Poincaré sphere (optics) Polarization ( also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of th ...

* Poincaré–Steklov operator *

Poincaré symmetry Poincaré is a French surname. Notable people with the surname include: * Henri Poincaré (1854–1912), French physicist, mathematician and philosopher of science * Henriette Poincaré (1858-1943), wife of Prime Minister Raymond Poincaré * Luc ...

* Poincaré wave

Other

Annales Henri Poincaré The ''Annales Henri Poincaré'' (''A Journal of Theoretical and Mathematical Physics'') is a peer-reviewed scientific journal which collects and publishes original research papers in the field of theoretical and mathematical physics. The emphasis ...

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 arrond ...

* Henri Poincaré Prize *

Henri Poincaré University The Henri Poincaré University, or Nancy 1, nicknamed UHP, was a public research university located in Nancy, France. UHP was merged into University of Lorraine in 2012, and was previously a member of the Nancy-Université federation, belongin ...

* 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 origina ...

* Poincaré Medal * Poincaré Seminars *

Books with the title "Henri Poincaré"

References

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