The Equivalence Problem for Systems of Second order Ordinary Differential Equations

Authors

Mark E. Fels, Utah State UniversityFollow

Document Type

Article

Journal/Book Title/Conference

Proc. London Math Soc.

Volume

71

Issue

3

Publication Date

1995

First Page

221

Last Page

240

Abstract

The equivalence problem for systems of second-order differential equations under point transformations is found to give rise to an {e}-structure of dimension n² + 4n + 3. It is then shown that the structure function for this {e}-structure is a differential function of two fundamental tensor invariants. The parametric forms of the fundamental invariants are given and their vanishing characterizes the trivial equation ¨xⁱ = 0. We also show that the vanishing of the fundamental invariants characterizes the unique system of second-order ordinary differential equations admitting a maximal-dimension Lie symmetry group. Thus, equations not equivalent to¨xⁱ =0 admit symmetry groups of dimension strictly less than n² + 4n + 3.

Recommended Citation

The equivalence problem for systems of second order ordinary deferential equations, Proc. London Math. Soc., M.E. Fels, 71(3), 1995, 221-240.