  Interrelations between dynamical and statistical laws in physics, on the one
hand, and between the classical and quantum mechanics, on the other hand, are
discussed with emphasis on the new phenomenon of dynamical chaos. The principal
results of the studies into chaos in classical mechanics are presented in some
detail, including the strong local instability and robustness of the motion,
continuity of both the phase space as well as the motion spectrum, and time
reversibility but nonrecurrency of statistical evolution, within the general
picture of chaos as a specific case of dynamical behavior. Analysis of the
apparently very deep and challenging contradictions of this picture with the
quantum principles is given. The quantum view of dynamical chaos, as an attempt
to resolve these contradictions guided by the correspondence principle and
based upon the characteristic time scales of quantum evolution, is explained.
The picture of the quantum chaos as a new generic dynamical phenomenon is
outlined together with a few other examples of such a chaos including linear
(classical) waves and digital computer. I conclude with discussion of the two
fundamental physical problems: the quantum measurement (\psi-collapse), and the
causality principle which both appear to be related to the phenomenon of
dynamical chaos.
