[Jacobi's bound for a diffiety defined by a quasi-regular system]
We show that Jacobi's bound for the order of a system of ordinary differential equations stands in the case of a diffiety defined by a quasi-regular system. We extend the result when there are less equations than variables and characterize the case when the bound is reached.
On montre que la borne de Jacobi pour l'ordre d'un système d'équations différentielles ordinaires est vraie dans le cas d'une diffiété définie par un système quasi régulier. Nous étendons le résultat au cas où il y a moins d'équations que d'inconnues et montrons que la non-nullité du jacobien tronqué est une condition nécessaire et suffisante pour que la borne soit atteinte.
Accepted:
Published online:
François Ollivier 1; Brahim Sadik 2
@article{CRMATH_2007__345_3_139_0, author = {Fran\c{c}ois Ollivier and Brahim Sadik}, title = {La borne de {Jacobi} pour une diffi\'et\'e d\'efinie par un syst\`eme quasi r\'egulier}, journal = {Comptes Rendus. Math\'ematique}, pages = {139--144}, publisher = {Elsevier}, volume = {345}, number = {3}, year = {2007}, doi = {10.1016/j.crma.2007.06.010}, language = {fr}, }
François Ollivier; Brahim Sadik. La borne de Jacobi pour une diffiété définie par un système quasi régulier. Comptes Rendus. Mathématique, Volume 345 (2007) no. 3, pp. 139-144. doi : 10.1016/j.crma.2007.06.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.06.010/
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