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Theses

Différentes modalités de travail sur le général dans les recherches de Poincaré sur les systèmes dynamiques

Abstract : What is a particular case ? How can a mathematician say that an event is «exceptionnal» and that, «generally», it does not occur ? This thesis asks those questions from an historical point of vue, throught the study of texts by Poincaré. The corpus taken in consideration has been build up around three centers: Poincaré's study of singular points of differential equations (1881), his work on the recurrence theorem (1889, 1890, 1891), and his memoir on geodesics of convex surfaces (1905). I considered what Poincaré called particular cases, exceptions. I examined the means he used in order to caracterise and study those cases, and the place he confer them.

Given the nature of the questions under examination, I had to develop a particular method of historical study, centered on systematical scrutiny of texts as such, and not only as conveying mathematical results. I examined the textual forms developped by Poincaré in order to express his results, the terminology he used, the links he set up between different results. That careful analysis throws a new light on texts some of which had already been studied by historians. Moreover, as it allows to describe how Poincaré is working in regard to the question of general, it reveals some features of his way of dealing as a mathematician.
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https://tel.archives-ouvertes.fr/tel-00011380
Contributor : Anne Robadey <>
Submitted on : Friday, January 13, 2006 - 6:21:05 PM
Last modification on : Thursday, December 10, 2020 - 11:09:03 AM
Long-term archiving on: : Saturday, April 3, 2010 - 9:23:25 PM

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Anne Robadey. Différentes modalités de travail sur le général dans les recherches de Poincaré sur les systèmes dynamiques. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2006. Français. ⟨tel-00011380⟩

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