Аннотация:Skew-symmetric differential forms possess unique capabilities that manifest
themselves in various branches of mathematics and mathematical physics.
The invariant properties of closed exterior skew-symmetric differential forms
lie at the basis of practically all invariant mathematical and physical
formalisms.
In present paper, firstly, the role of closed exterior skew-symmetric differential forms is illustrated, and, secondly, it is shown that there exist evolutionary skew-symmetric differential forms that generate closed exterior differential forms.
The process of extracting closed exterior forms from evolutionary forms enables one to describe discrete transitions, quantum jumps, the generation of various structures,
origination of such formations as waves, vortices and so on.
In none of other mathematical formalisms such proceses can be described
since their description includes degenerate transformations and
transitions from nonintegrable manifolds to integrable ones.