ИСТИНА

The normal form method is based on a transformation of an ODEs system to a simpler set called the normal form. The importance of this method for an analyzing of ODEs near stationary point has been recognized for a long time. For the history of this subject see, for instance, (Arnold, Anosov, 1988) or (Guckenheimer, Holmes, 1986). Definitions of normal form and normalizing transformation can be formulated in different ways for general and special cases. So there are very developed approaches for Hamiltonian systems, see, for example, (Deprit, 1969), (Hori, 1966), (Bruno, 1971, 1972), (Bruno, 1994, chapters 1, 2). For resonant and Belitskii normal forms see (Bruno, 1998, 2000, chapter 5, $ 20), (Bibikov, 1979).