Jean Écalle (born 1947) is a French mathematician, specializing in dynamic systems, perturbation theory, and analysis.
Écalle received, in 1974 from the University of Paris-Saclay in Orsay, a doctorate under the supervision of Hubert Delange with Thèse d'État entitled La théorie des invariants holomorphes.
[2][3][4] Écalle's theory has important applications to solutions of generalizations of Abel's integral equation; the method of resurgent functions provides for such solutions a (Borel) resummation method for dealing with divergent series arising from semiclassical asymptotic developments in quantum theory.
[5] He applied his theory to dynamic systems [6] and to the interplay between diophantine small denominators and resonance involved in problems of germs of vector fields.
In 1988 Écalle was the inaugural recipient of the Prix Mergier-Bourdeix [fr] of the Académie des Sciences.