Geodesic
Poincaré's early use of Analysis situs in nonlinear differential equation : variations around the theme of Kronecker's integral
Mawhin, Jean1 
1 Université de Louvain, Institut mathématique
Philosophia Scientiae, Contributions à l’histoire des mathématiques au XIXe siècle, Tome 4 (2000) no. 1, pp. 103-143

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We analyze the chronological and conceptual evolution of the early use by Poincaré of Analysis situs tools, and in particular of Kronecker's index in his qualitative theory of nonlinear differential equations. We show in this way that prior to his famous series of subsequent papers on Analysis situs, Poincaré had already obtained or anticipated many important topological results.

Nous analysons l'évolution chronologique et conceptuelle des premières apparitions d'outils d'Analysis situs, et en particuluer de l'indice de Kronecker, dans la théorie qualitative des équations différentielles de Poincaré. Nous montrons ainsi que, bien avant sa fameuse série de mémoires sur l'Analysis situs, Poincaré avait déjà obtenu ou anticipé de nombreux résultats importants de topologie.

Mawhin, Jean 1

1 Université de Louvain, Institut mathématique 
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     title = {Poincar\'e's early use of {\protect\emph{Analysis} situs} in nonlinear differential equation : variations around the theme of {Kronecker's} integral},
     journal = {Philosophia Scientiae},
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     publisher = {\'Editions Kim\'e},
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Mawhin, Jean. Poincaré's early use of Analysis situs in nonlinear differential equation : variations around the theme of Kronecker's integral. Philosophia Scientiae, Contributions à l’histoire des mathématiques au XIXe siècle, Tome 4 (2000) no. 1, pp. 103-143. http://geodesic.mathdoc.fr/item/PHSC_2000__4_1_103_0/