Abstract. A set of new ideas and concepts (which the authors treat as a new version of the theory of hierarchic dynamic systems) are set forth in the article. In turn, the set of hierarchic principles is put in the methodogical basis of this theory. It is shown, a peculiar version of the theory of hierarchic waves and oscillations can be developed on the basis of proposed general theory.

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The results of analysis of the electron undulative induction accelerator are presented in the paper. It is shown, in particular, that a wide spectrum of technological systems (destined for natural and wastewater purification, medicine equipment and preparations, etc.) can be constructed on the basis of undulative induction accelerator. Characteristic features of these systems are commercial attractiveness, high level of efficiency and relative compactness. One variant of design of the undulative induction accelerator is described and discussed.