The book consists of two Volumes. The first (the preceding volume) is
devoted to the general nonlinear theory of the hierarchical dynamic
oscillative-wave systems. This theory has been called the theory of hi-
archical oscillations and waves. Here two aspects of the proposed theory
are discussed. The first aspects concern the fundamental nature and the
basic c- cepts and ideas of a new hierarchical approach to studying
hierarchical dynamic systems. A new hierarchical paradigm is proposed as
a - sis of a new point of view of such types of systems. In turn, a set
of hierarchical principles is formulated as the fundamental basis of
this paradigm. Therein the self-resemblance (holographic) principle
plays a key role here. An adequate mathematic description
(factorization) of the proposed paradigm is carried out. The concepts of
structural and dynamic (functional) operators are put into the basis of
this descr- tion. Electrodynamics is chosen as a convenient basis for an
obvious demonstration of some key points of the proposed new theory. The
second aspect has a purely mathematical nature. It is related to the
form of factorization (i.e., mathematical description) of hier- chical
types of dynamic models, and discussion of the methods of their
mathematical analysis. A set of the hierarchical asymptotic analytical-
numerical methods is given as an evidence of the practical effectiveness
of the proposed version of hierarchical theory.
