  It is argued that the world is a dissipative dynamic system, a phase flow of
which is formed by conformally-symplectic mapping. The key assumption is that
the concept of energy in microcosm makes sense only for the steady motions
corresponding to quantum eigenstates. The constant, which determines the
exponential phase volume contraction, is supposed to be a new universal
constant, in addition to the speed of light and Planck constant. It is shown
that statistical treatment of quantum objects as the ensembles concentrated on
smooth connected attractors provides a simple explanation of stochastic
behaviour of these objects as well as leads to a natural interpretation of the
wave function, stationary Schrodinger equation, and scattering matrix. To
validate the general hypotheses stated in the work, some physical models are
presented. In particular, the models support the view that the inertial motion
and quantum properties are basically determined by the vacuum as a dynamic
subsystem. The matter-vacuum interaction is described formally by means of
multivalued Hamilton function. A drawback of all these models is the
non-locality of equations of motion stemming from the non-locality of variation
of multivalued Hamilton function. This drawback can be overcome in the field
theory using multivalued functionals with a local first variation opened by S.
P. Novikov. Hence, a prospect of construction of the unified field theory in
Einstein spirit, without a procedure of quantization is opened.
