  The universal dynamic uncertainty, discovered in Parts I and II of this
series of papers for the case of Hamiltonian quantum systems, is further
specified to reveal the hierarchical structure of levels of dynamically
redundant 'realisations' which takes the form of the intrinsically
probabilistic 'fundamental dynamical fractal' of a problem and determines
fractal character of the observed quantities. This intrinsic fractality is
obtained as a natural, causally derived property of dynamic behaviour of a
system with interaction and the corresponding complete solution. Every branch
of the fundamental dynamical fractal of a problem, as well as the probability
of its emergence, can be obtained within the extended nonperturbative analysis
of the main dynamic equation (Schroedinger equation in our case), contrary to
basically restricted imitations of fractality within the canonical,
single-valued approach. The results of the dynamical chaos analysis in
Hamiltonian quantum systems, Parts I-III, are then subjected to discussion and
generalisation. The physical origins of the dynamic uncertainty are analysed
from various points of view. The basic consequences, involving essential
extension of the conventional, unitary (= single-valued) quantum mechanics, are
summarised. Finally, we emphasize the universal character of the emerging
notions of dynamic multivaluedness (or redundance), causal randomness (or
dynamic uncertainty), first-principle probability, (non)integrability, general
solution, and physical complexity applicable to real dynamical systems of any
kind.
