Henri Poincaré

Résumé

Henri Poincaré est un mathématicien, physicien théoricien et philosophe des sciences français, né le à Nancy et mort le à Paris. Poincaré a réalisé des travaux d'importance majeure en optique et en calcul infinitésimal. Ses avancées sur le problème des trois corps en font un fondateur de l'étude qualitative des systèmes d'équations différentielles et de la théorie du chaos ; il est aussi un précurseur majeur de la théorie de la relativité restreinte et de la théorie des systèmes dynamiques. Il est considéré comme un des derniers grands savants universels, maîtrisant l'ensemble des branches des mathématiques de son époque et certaines branches de la physique. Biographie Henri Poincaré est le fils d'Émile Léon Poincaré, doyen de la faculté de médecine de Nancy, et de son épouse Marie Pierrette Eugénie Launois. Il est le neveu d'Antoni Poincaré, ce qui en fait le cousin germain des fils de ce dernier : l'homme politique et président de la Répub

Source officielle

https://fr.wikipedia.org/wiki/Henri_Poincar%C3%A9

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Cours associés (21)

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.

The course is about the derivation, theoretical analysis and implementation of the finite element method for the numerical approximation of partial differential equations in one and two space dimensions.

The goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals.

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Séances de cours associées (37)

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L'espace contre l'architecture

Grégory Azar

This research work analyses Theo van Doesburg's Counter-constructions presented in Paris in 1923 at the "L'Effort Moderne" exhibition. These Counter-constructions stand as icons of the Modern Movement due to their role as precursors of a new "boundless" spatiality, a role first intuitively perceived by Le Corbusier or Mies van der Rohe and then theorized by Sigfried Giedion. We have attempted in this research a theoretical study of the Counter-constructions' position within the architectural field. That is to say bringing together their aspect of "spatial manifest" and the Dadaist persona of Theo van Doesburg; this alleged contradiction between the progressive and negative dimension of the Counter-constructions being the subject of this research. It is based on the following problematic: understanding what is at stake in the disjointing of the polychrome plane (as a textile surface) and the suppression of the architectural boundary under the guise of spatial continuity ("the breaking of the enclosure" mentioned by Theo van Doesburg and his interest in the notion of mathematical continuum through the theories of the fourth dimension: Henri Poincaré's Analysis situs). That amounts to studying the modalities connecting the notions of dressing and of continuum to a destructive drive, "throwing out" the inside of the house. The methodology turns towards psychoanalysis through the concepts of Verneinung [negation] (Freud) and Moi-peau [Skin-ego] (Anzieu).

EPFL2005

Chargement

We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar, equations on Lie groups and homogeneous spaces. Orbit invariants play an important role in this context and we use these invariants to prove global existence and uniqueness results for a class of PDE. This class includes Euler-Poincar, equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, mu CH and mu DP equations, and the geodesic equations with respect to right-invariant Sobolev metrics on the group of diffeomorphisms of the circle.

Springer Netherlands2011

Chargement

Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Grégoire Aubry

The Uniformization Theorem due to Koebe and Poincaré implies that every compact Riemann surface of genus greater or equal to 2 can be endowed with a metric of constant curvature – 1. On the other hand, a compact Riemann surface is a complex algebraic curve and is therefore described by a polynomial equation with complex coefficients. The uniformization problem is then to link explicitly these two descriptions. In [BS05b], Peter Buser and Robert Silhol develop a new uniformization method for compact Riemann surfaces of genus two. Given such a surface S, the method describes a polynomial equation of an algebraic curve conformally equivalent to S. However, in this method appear a complex number τ BS and a function f BS which is holomorphic on the unit disk, both being characterized by some functional equations. This means that τ BS, f BS are given implicitly. P. Buser and R. Silhol then approximate them numerically by a complex number τ and a polynomial p using the approximation method developped in [BS05a]. In cases where the equation of the algebraic curve is known, they notice that these approximations are very good. In this thesis we prove a convergence theorem for the approximation method of P. Buser and R. Silhol, and we propose an adaptation of their method that allows to solve some of the numerical problems to which it is prone. Moreover, we generalize this uniformization method to hyperelliptic Riemann surfaces of genus greater than 2, and we give some examples of numerical uniformization in genus 3.

EPFL2010

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