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Poincares approach to the three body problem has often been celebrated as a starting point of chaos theory in relation to the investigation of dynamical systems. Yet, Poincares strategy can also be analyzed as molded on - or casted in - some specific algebraic practices for manipulating systems of linear equations. These practices shed new light on both the novelty and the collective dimensions of Poincares Methodes nouvelles. As the structure of a cast-iron building may be less noticeable than its creative fac{c}ade, the algebraic cast of Poincares strategy is broken out of the mold in generating the novel methods of celestial mechanics. But as the various components that are mixed in some casting process can still be detected in the resulting alloy, the algebraic cast of the Methodes nouvelles points to some collective dimensions of Poincares methods. An edited version of the present preprint is to be published in the journal textit{Lastronomie} under the title Lapproche de Poincar`E sur le problEme des trois corps. This publication is an abstract in French language of a forthcoming paper - The algebraic cast of Poincar`Es textit{M`Ethodes nouvelles} - which will develop its main claims as well as the historiographical and mathematical issues raised in section 4 and section 5.
This paper aims at shedding a new light on the novelty of Poincares Methodes nouvelles de la mecanique celeste. The latters approach to the three-body-problem has often been celebrated as a starting point of chaos theory in relation to the investigat
The legacy of Jordans canonical form on Poincares algebraic practices. This paper proposes a transversal overview on Henri Poincares early works (1878-1885). Our investigations start with a case study of a short note published by Poincare on 1884 : S
What did algebra mean before the development of the algebraic theories of the 20th century ? This paper stresses the identities taken by the algebraic practices developped during the century long discussion around the equation around the equation of
Dirichlet proves the general convergence of Fourier series, after pointing out errors in an earlier attempt by Cauchy. We transcribed from Crelles Journal (1829) with numerous typographical corrections, and added a completed bibliography. Dirichlet
The principal result of this work is the freeness in the $ overline{mathbb Z}_l$-cohomology of the Lubin-Tate tower. The strategy is of global nature and relies on studying the filtration of stratification of the perverse sheaf of vanishing cycles of