Tartu University,

Puhta Mathematical Institute,

J. Liivi 2-427, 50409 Tartu, ESTONIA

E-mail: rahula@math.ut.ee

**Universal structure of jet space**

**Abstract:**

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.

**References:**

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