Danylenko O. Orbital approach and (C,F)-construction in ergodic theory

Objects: dynamical sysyems. Goals: to solve a number of problems in ergodic theory using orbital methods in a systematic way; construction a number of substancial examples of dynamical systems in the framework of the (C,F)-construction. Methods: methods of orbit theory, general topology, functional analysis, spectral theory, theory of measure. New theoretical results: entropy theory for cocycles of ergodic equivalent relations is constructed, concrete examples of ergodic transformations with homogeneous spectrum of arbitrary multiplicity are constructed, a new construction of mixing actions of rank one is developed, a theory of near simple actions is developed. Applications. The results may be applied in entropy theory, spectral theory, when constructing funny rank one actions possessing various dynamical properties, to study cocycles of ergodic equivalence relations.