We give a new proof of Jouanolou's theorem about non-existence of algebraic solutions to the system x: = z(s), y = z(s), z = y(s). We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.
机构:
Russian Acad Sci, Steklov Math Inst, Moscow 119991, Russia
Univ Liverpool, Liverpool L69 3BX, Merseyside, EnglandRussian Acad Sci, Steklov Math Inst, Moscow 119991, Russia