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\title{On the generators of the New Perturbation Methods}

\author{Grebenikov, A. A.}
\address{Moscow}


\begin{abstract}
The mathematical models for nature study problems are described by
nonlinear, more often, by differential equations, solutions of which,
as a rule, not represented by the compact analytical form. For this
reason, Newton, Euler, Clairaut, Lagrange, Laplace, Poincar\'e and
other scientists proposed to search for these solutions by means of  
iterative methods, that is, series, approximations and transformations.
These methods were realised, first of all, in classical astronomy
(celestial mechanics and astrometry). It should be emphasized, that the
constructive theory, of nonlinear equations, based on iterative
methods, dominates in the modern nonlinear analysis.

My reprint is based on these ideas and is concerned with one
interpretation of the classical and modern perturbation theory for
differential equations with small parameter.
\end{abstract}
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