Poincaré then went on to consider Le Sage's theory in the context of the " new dynamics " that had been developed at the end of the 19th and the beginning of the 20th centuries, specifically recognizing the relativity principle.

Chaos theory and the sensitive dependence on initial conditions was described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.

The work of Lorentz was mathematically perfected by Henri Poincaré who formulated on many occasions the Principle of Relativity and tried to harmonize it with electrodynamics.

At the beginning of the 20th century, Henri Poincaré was working on the foundations of topology — what would later be called combinatorial topology and then algebraic topology.

Poincaré claimed in 1900 that homology, a tool he had devised based on prior work by Enrico Betti, was sufficient to tell if a 3-manifold was a 3-sphere.

Hamilton's program was started in his 1982 paper in which he introduced the Ricci flow on a manifold and showed how to use it to prove some special cases of the Poincaré conjecture.

* John Morgan and Gang Tian posted a paper on the arXiv in July 2006 which gave a detailed proof of just the Poincaré Conjecture ( which is somewhat easier than the full geometrization conjecture ) and expanded this to a book.

John Morgan spoke at the ICM on the Poincaré conjecture on August 24, 2006, declaring that " in 2003, Perelman solved the Poincaré Conjecture.

In December 2006, the journal Science honored the proof of Poincaré conjecture as the Breakthrough of the Year and featured it on its cover.

Hamilton's program for proving the Poincaré conjecture involves first putting a Riemannian metric on the unknown simply connected closed 3-manifold.

In November 2002, Russian mathematician Grigori Perelman posted the first of a series of eprints on arXiv outlining a solution of the Poincaré conjecture.

* The Geometry of 3-Manifolds ( video ) A public lecture on the Poincaré and geometrization conjectures, given by C. McMullen at Harvard in 2006.

* The slides used by Yau in a popular talk on the Poincaré conjecture.

Conventions which used the Franc Poincaré included the Convention for the Unification of Certain Rules Relating to International Carriage by Air, the International Convention on Civil Liability for Oil Pollution Damage and the International Convention on the Establishment of an International Fund for Compensation for Oil Pollution Damage.

Likewise, Banach's fixed point theorem, based on earlier methods developed by Charles Émile Picard, was included in his dissertation, and was later extended by his students ( for example in the Banach – Schauder theorem ) and other mathematicians ( in particular Bouwer and Poincaré and Birkhoff ).

In his autobiography, mathematician Gian-Carlo Rota tells of casually browsing the mathematical stacks of Sterling Library and stumbling on a handwritten mailing list, attached to some of Gibbs's course notes, which listed over two hundred notable scientists of his day, including Poincaré, Hilbert, Boltzmann, and Mach.

One of the major innovations made by the Salon Cubists, independently of Picasso and Braque, was that of simultaneity, drawing to greater or lesser extent on theories of Henri Poincaré, Ernst Mach, Charles Henry, and Henri Bergson.

Other famous problems on his list include the Poincaré conjecture, the P = NP problem, and the Navier-Stokes equations, all of which have been designated Millennium Prize Problems by the Clay Mathematics Institute.

where σ is a 3-vector composed of the Pauli matrices ( used here as generators for the Lie group SL ( 2, C )) and n and m are real 3-vectors on the Poincaré sphere corresponding to one of the propagation modes of the medium.

* Poincaré recurrence theorem, Henri Poincaré's theorem on dynamical systems

Henri Poincaré gave a keynote address on mathematical physics, including an outline for what would eventually became known as special relativity.

Following the armistice with Germany ending the First World War, the French army entered Metz in November 1918 and Philippe Pétain received his marshal's baton from French President Raymond Poincaré and Prime Minister Georges Clémenceau on the Esplanade garden.

The error ( which also appears in the note of a Mr. Richard in the last issue of the Acta mathematica, which Mr. Poincaré emphasizes in the last issue of the Revue de Métaphysique et de Morale ) is, in my opinion, the following: It is assumed that the system

Already in his philosophical writing on time measurements ( 1898 ) Poincaré wrote that astronomers like Ole Rømer, in determining the speed of light, simply assume that light has a constant speed, and that this speed is the same in all directions.

( The defining symmetry of special relativity is the Poincaré group which also includes translations and rotations.

The more general set of transformations that also includes translations is known as the Poincaré group.

In the same paper, Poincaré wondered whether a 3-manifold with the homology of a 3-sphere and also trivial fundamental group had to be a 3-sphere.

In 1958 Bing proved a weak version of the Poincaré conjecture: if every simple closed curve of a compact 3-manifold is contained in a 3-ball, then the manifold is homeomorphic to the 3-sphere .< ref > Bing also described some of the pitfalls in trying to prove the Poincaré conjecture.

Special relativity ( SR, also known as the special theory of relativity or STR ) is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein ( after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others ) in the paper " On the Electrodynamics of Moving Bodies ".

They also engaged the work of contemporary philosophers and scientists, such as Karl Pearson, Ernst Mach, Henri Poincaré, William James and John Dewey in an attempt to move, in the words of Boas ' student Robert Lowie, from " a naively metaphysical to an epistemological stage " as a basis for revising the methods and theories of anthropology.

Poincaré dodecahedral space ( PDS ), but horn topologies ( which are hyperbolic ) were also deemed compatible with the data.

* Henri Poincaré University ( Université Henri Poincaré, UHP, also known as Nancy 1 )

The cotangent bundle carries a tautological one-form θ also known as the Poincaré 1-form or Liouville 1-form.

Mathematician and physicist Henri Poincaré made important contributions to pure and applied mathematics, and also published books for the general public on mathematical and scientific subjects.

This gives an upper bound on the absolute values of the eigenvalues of Frobenius, and Poincaré duality then shows that this is also a lower bound.

It also plays an important role in hyperbolic geometry, where the Poincaré half-plane model provides a way of examining hyperbolic motions.

It also maps the interior of the unit sphere to itself, with points outside the orthogonal sphere mapping inside, and vice-versa ; this defines the reflections of the Poincaré disc model if we also include with them the reflections through the diameters separating hemispheres of the unit sphere.

Raymond was also the cousin of Henri Poincaré, the famous mathematician.

Jules Henri Poincaré ( 1854 – 1912 ), also a distinguished physicist and mathematician, belonged to another branch of the same family.

For this reason, in this context, the symplectic structure is also called Poincaré invariant.

By interpreting the upper half of the complex plane as a model of the hyperbolic plane ( the Poincaré half-plane model ) Ford circles can also be interpreted as a tiling of the hyperbolic plane by horocycles.

The Whitney trick was used by Steve Smale to prove the h-cobordism theorem ; from which follows the Poincaré conjecture in dimensions, and the classification of smooth structures on discs ( also in dimensions 5 and up ).

See also Poincaré map.

A simple argument using the exponential exact sequence and the d-bar Poincaré lemma shows that it also admits no non-trivial holomorphic vector bundles.

Thus, Poincaré duality says that and are isomorphic, although there is no natural map giving the isomorphism, and similarly and are also isomorphic, though not naturally.