Tartu University,
Puhta Mathematical Institute,
J. Liivi 2-427, 50409 Tartu, ESTONIA

Universal structure of jet space

1. The operator D (of total derivative) in infinite jet space is a linear vector field. Exponential law determines his flow.
2. The same exponential law permits to calculate invariants of D.
3. The Lie field P (infinitesimal symmetry of D) can be studied in three different basis:
        a) in natural basis after Lie-Olver [1], approach classic,
        b) in adapted basis after Vinogradov [2], approach with contact forms and generating functions,
        c) in invariant basis [3].
The exponential law promises a new invariant method for study of differential operators and equations and singularities.


  1. Olver, P.J., Applications of Lie Groups to Differential Equations, S-V, 1993, 510 pp.
  2. Vinogradov, A.M., Krasil'shchik, I.S.(ed), Symmetries and Conservation Laws of Mathematical Physics, Moscow, 1997, 462 pp.
  3. Rahula, M., New Problems in Differential Geometry, WS, 1993, 172 pp.