# zbMATH — the first resource for mathematics

Singularities of solutions, spectral sequences and normal forms of Lie algebras of vector fields. (Russian) Zbl 0643.58039
This paper gives a general method of finding conditions of formal solvability of systems of differential equations in a class of functions with singularities. The author investigates here a formal linearization of an action of Lie algebra of vector fields; in particular the algebras of contact and Hamiltonian vector fields are considered. For a semisimple, reductive or commutative Lie algebra he obtains conditions for a formal equivalence to imply a $$C^{\infty}$$- or $$C^{\omega}$$- equivalence.
The results of this paper were announced in Dokl. Akad. Nauk SSSR 251, 794-799 (1980; Zbl 0475.58026) and Usp. Mat. Nauk 38, No.5(233), 199-200 (1983; Zbl 0552.58008).
Reviewer: W.Mozgawa

##### MSC:
 58J99 Partial differential equations on manifolds; differential operators 17B65 Infinite-dimensional Lie (super)algebras 17B56 Cohomology of Lie (super)algebras