Algebraical aspects of parametrical decomposition method

The paper focuses on the approach based on precise analytical methods of research for nonlinear dynamical systems with a complex structure of the state space. This method allows to analyze behavior of essentially multivariable systems through the dynamic behavior of its basic components, i.e., subsystems (both linear and nonlinear), that have a reduced order state-space. Such approach allows to bring out strict proof of existence of free and forced periodical motions. In most cases the approach allows to complete “partition” of the space of parameters into areas corresponding to qualitatively different dynamic behaviors.