Jean Écalle

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Jean Écalle (* 1950 ) is a French mathematician who specializes in dynamic systems, perturbation theory and analysis.

Ecalle received his doctorate in 1974 under Hubert Delange at the University of Paris-Süd in Orsay (Thèse d`Etat: La théorie des Invariants holomorphes ). He is Research Director of the Center national de la recherche scientifique (CNRS) and is a professor at the University of Paris-South.

He developed a theory of his so-called Resurgenter functions , analytic functions with isolated singularities which a special algebra of derivatives ( Alien Calculus , Calcul différentiel étranger possess) to its various singularities in slightly modified form rise again (hence the name). One example are the solutions to Abel's integral equation . It provides a (Borel) resummation method for divergent series for this functional class, for example from asymptotic developments, with application to the semiclassical development in quantum theory.

He applied his theory to dynamic systems and to resonances (the problem of the small denominator).

Independently of Juli Ilyashenko , he proved that the number of limit cycles of polynomial vector fields in the plane is finite, which Henri Dulac tried to prove in 1923. This is related to the 16th Hilbert problem .

He was invited speaker at the 1990 International Congress of Mathematicians in Kyoto ( The acceleration operators and their applications ). In 1988 he was the first to receive the Prix ​​Mergier-Bourdeix of the Académie des Sciences.

Fonts

  • Les Fonctions Résurgentes , 3 volumes, pub. Math. Orsay, 1985
  • Cinq applications des fonctions résurgentes , Pub. Math. Orsay 1984
  • Singularités non abordables par la géométrie , Annales Inst. Fourier, 42, 1992, 73-164, numdam
  • Six Lectures on Transseries, Analyzable Functions and the Constructive Proof of Dulac's Conjecture , in D. Schlomiuk Bifurcations and Periodic Orbits of Vector Fields , Kluwer 1993, 75-184
  • with B. Vallet Correction, and linearization of resonant vector fields or diffeomorphisms , Mathematische Zeitschrift 229, 1998, pp. 249-318
  • A Tale of Three Structures: the Arithmetics of Multizetas, the Analysis of Singularities, the Lie Algebra ARI , in BLJ Braaksma, GK Immink, Marius van der Put, J. Top (Editor) Differential Equations and the Stokes Phenomenon , World Scientific 2002, Pp. 89-146.
  • Recent Advances in the Analysis of Divergence and Singularities , in C. Rousseau, Yu. Ilyasheenko (editor) Proceedings of the July 2002 Montreal Seminar on Bifurcations, Normal forms and Finiteness Problems in Differential Equations , Kluwer 2004, pp. 87-187
  • Theory of the Invariants Holomorphes , Pub. Math. Orsay 1974
  • Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac , Paris: Hermann 1992
  • Six lectures on trousseries, analysable functions and the construtive proof of Dulac's conjecture , in: D. Schlominck, Bifurcations and periodic orbits of vector fields, Kluwer 1993, pp. 75-184

Web links

Individual evidence

  1. ↑ Jean Écalle in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Introduction z. B. Sauzin Resurgent functions and splitting theorem , 2007 , Boris Sternin, Victor Shatalov Borel-Laplace Transform and Asymptotic Theory: Introduction to Resurgent Analysis , CRC Press 1996, Bernard Malgrange Introduction aux travaux de J. Ecalle , L´Enseignement Mathématique, 31, 1985, 261-282
  3. ↑ Frédéric Pham Introduction à la résurgence quantique, d'après Ecalle et Voros , Séminaire Bourbaki 656, 1985/86, Online ( Memento of the original from April 20, 2015 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.numdam.org
  4. ↑ Bernard Malgrange , Travaux d'Ecalle et de Martinet - Ramis sur les systèmes dynamiques, Séminaire Bourbaki 582, 1981/82, Online ( Memento of the original from September 27, 2013 in the Internet Archive ) Info: The archive link was inserted automatically and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.numdam.org
  5. ↑ Ecalle Singularités non abordables par la géométrie , Ann. Inst. Fourier, 42, 1992, 73
personal data
SURNAME Écalle, Jean
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH 1950