Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations

Abstract

CONTENTSIntroductionChapter I. Dulac's theorem and its generalization § 1. Definitions § 2. Reduction of the finiteness problem to the study of a neighbourhood of a compound cycle with elementary singular points § 3. Correspondence maps § 4. Composition of correspondence maps § 5. Remarks on Dulac's theory § 6. Two finiteness theoremsChapter II. Smooth orbital classification of elementary singular points of plane vector fields § 1. Survey of known results and sketch of a proof of the classification theorem § 2. Formal normal forms § 3. Proof of the classification theorem for degenerate elementary singular pointsConclusionAppendix. Example of a flat quadratic system having four limit cycles (after Shi Sonling)References