Equivalence of differential equations and differential algebras

Rok, strany: 1994, 125 - 130

In a space of nonlinear ordinary differential equations we consider two equivalence relations. Static equivalence means equivalence up to nonlinear transformations of dependent variables. A much weaker dynamic equivalence uses transformations which depend on dependent variables and their derivatives up to finite order (this relation is closely related to Cartan's absolute equivalence). To each system of ODE's we assign a differential algebra which is a commutative associative algebra with a derivation. This algebra is equiped with a natural filtration. Our first result says that two systems are dynamically equivalent if and only if their differential algebras are isomorphic. Our second result states that two systems are statically equivalent if and only if their filtered differential algebras are isomorphic.

ISO 690:

Jakubczyk, B. 1994. Equivalence of differential equations and differential algebras. In Tatra Mountains Mathematical Publications, vol. 4, no.1, pp. 125-130. 1210-3195.

APA:

Jakubczyk, B. (1994). Equivalence of differential equations and differential algebras. Tatra Mountains Mathematical Publications, 4(1), 125-130. 1210-3195.