Les derniers travaux de Jean Martinet
Ramis, Jean-Pierre
Annales de l'Institut Fourier, Tome 42 (1992), p. 15-47 / Harvested from Numdam
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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

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.

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     author = {Ramis, Jean-Pierre},
     title = {Les derniers travaux de Jean Martinet},
     journal = {Annales de l'Institut Fourier},
     volume = {42},
     year = {1992},
     pages = {15-47},
     doi = {10.5802/aif.1285},
     mrnumber = {94m:01035},
     zbl = {0927.01031},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1992__42_1-2_15_0}
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Ramis, Jean-Pierre. Les derniers travaux de Jean Martinet. Annales de l'Institut Fourier, Tome 42 (1992) pp. 15-47. doi : 10.5802/aif.1285. http://gdmltest.u-ga.fr/item/AIF_1992__42_1-2_15_0/

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