Les derniers travaux de Jean Martinet
Annales de l'Institut Fourier, Volume 42 (1992) no. 1-2, pp. 15-47.

Gevrey classes theory and summability are natural generalizations of Cauchy theory. We use a little bit of Non Standard Analysis and we introduce ε-functions (for ε>0, infinitely small, fixed, and ε-function is a holomorphic function defined “up to ε”, and “not too big”). We extend Cauchy theory to ε-functions and get wild Cauchy theory. The wild analytic continuation principle is one of the central results. We interpret delays in bifurcations using Gevrey asymptotics.

On montre comment la théorie des classes de Gevrey et de la sommabilité sont des généralisations naturelles de la théorie de Cauchy. On utilise le vocabulaire de l’Analyse Non Standard et on introduit la notion d’ε-fonction (fonction analytique définie “à ε près”, pour ε>0 infiniment petit fixé, et ne prenant que des valeurs infiniment petite devant 1/ε. On étend la théorie de Cauchy aux =FDe-fonctions  : c’est la théorie de Cauchy sauvage. On interprète le phénomène de retard à la bifurcation à l’aide d’asymptoticité Gevrey

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Ramis, Jean-Pierre. Les derniers travaux de Jean Martinet. Annales de l'Institut Fourier, Volume 42 (1992) no. 1-2, pp. 15-47. doi : 10.5802/aif.1285. https://aif.centre-mersenne.org/articles/10.5802/aif.1285/

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