The first part of this volume is an exposition of the theory of "systèmes en involution" of É. Cartan, from the homological point of view of Spencer, Sternburg et al. The point of view of Cartan himself is also recalled, and compared to the preceding one, in Appendix B. The second part proves the generic involutiveness of analytic differential systems, which is a precise version of an assertion of Cartan saying roughly that, "by prolongation, a differential system becomes eventually involutiveness".

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in analysis.

Table of Contents

• Introduction
• Modules gradués, involutivité
• Systèmes différentiels: théorie formelle
• Le théorème de Cartan-Kähler
• \(D\)-variétés
• Involutivité générique (suite)
• Variétés affines
• Invoutivité à la Cartan
• Bibliographie