Classification of Certain Class of Ordinary Differential Equations of the First Order
We study problem of global classification of ordinary differential equations with the linear-fractional right-hand side with rational coefficients with respect to a symmetry group. We find the field of differential invariants and obtain the equivalence criterion for two such equations. We adduce certain examples for applying of this criterion. These examples were obtained by means of computer.
Keywordsordinary differential equations differential invariant jet space algebraic geometry
Unable to display preview. Download preview PDF.
- 2.Kruglikov, B. S. “Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond”, Proceedings of the Fifth Abel Symposium, Tromso, Norway, June 17–22 (Springer, Berlin, 2009), 199–221.Google Scholar
- 3.Bibikov, P. “On Lie Problem and Differential Invariants of the Equations y = F(x, y)”, Func. Analyzis and Appl. (in press).Google Scholar
- 4.Bibikov, P., Malakhov, A. “On Lie Problem and Differential Invariats for the Subgroup of the Plane Cremona Group”, J. Geom. and Phys. (in press).Google Scholar