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The last works of Jean Martinet. (Les derniers travaux de Jean Martinet.) (French) Zbl 0927.01031

Summary: Gevrey classes theory and summability are natural generalizations of Cauchy theory. We use a little bit of Non Standard Analysis and we introduce \(\varepsilon\)-functions (for \(\varepsilon>0\), infinitely small, fixed, and \(\varepsilon\)-function is a holomorphic function defined “up to \(\varepsilon\)”, and “not too big”). We extend Cauchy theory to \(\varepsilon\)-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.

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
01A60 History of mathematics in the 20th century
03H05 Nonstandard models in mathematics
58-03 History of global analysis

Biographic References:

Martinet, Jean
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References:

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