Scaling regularities of similarity of periodical motions in nonlinear dynamical systems

Analysis of evolution and scale properties of subharmonic motions of dissipative and conservative nonlinear oscillators with one degree of freedom at transition from regular to chaotic regimes of motion through sequence of bifurcations is carried out. The numerical technique of research is based on a combination of methods of continuation of a solution by parameter, stability criterions, theory of branching, theory of scaling and precise methods of numerical integration. A number of universal scaling regularities, qualitatively and quantitatively describing transformation of the system phase space on a threshold of chaos, is revealed.