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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 1997, том 2, выпуск 3-4, страницы 170–178 (Mi rcd1018)

On the 60th birthday of V.I.Arnold

Scaling regularities of similarity of periodical motions in nonlinear dynamical systems

V. I. Guliaev, T. V. Zavrazhina

Ukrainian Transport University, Kiev State Technical University of Building and Architecture, Ukraine

Аннотация: 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.

Поступила в редакцию: 20.08.1997

Язык публикации: английский

DOI: 10.1070/RD1997v002n04ABEH000056



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