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Approach to resurgence. (Approche de la résurgence.) (French) Zbl 0791.32001
Actualités Mathématiques. Paris: Hermann, Éditeurs des Sciences et des Arts. 289 p. (1993).
The underlying book presents an elementary introduction to the theory of “resurgent functions” developed by J. Ecalle. This theory goes back to Borel’s procedure of summation of divergent series. The book consists of a prologue, two main parts, and an epilogue. While the prologue and epilogue describe the main ideas of the approach combined in the “strange calculus”, the second chapter titled “Resurgence” gives a systematic exposition of the theory of “resurgent functions”. The first chapter contains necessary results for the “resurgence” from the single variable complex analysis.
Reviewer: A.Isaev (Canberra)

32-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces
32A05 Power series, series of functions of several complex variables
34D05 Asymptotic properties of solutions to ordinary differential equations
32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30-XX)
30B50 Dirichlet series, exponential series and other series in one complex variable
30B40 Analytic continuation of functions of one complex variable
32D99 Analytic continuation