ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kuznetsov A. P., Kuznetsov S. P., lvankov N. Y., Osin A. A. Scaling at the transition to chaos via destruction of quasiperiodic motion at the golden mean frequency ratio. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 4, pp. 3-24. DOI: 10.18500/0869-6632-2000-8-4-3-24

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Language: 
Russian
Heading: 
Review of Actual Problems of Nonlinear Dynamics
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2000-8-4-3-24

Scaling at the transition to chaos via destruction of quasiperiodic motion at the golden mean frequency ratio

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
lvankov Nikolay Yurevich, Saratov State University
Osin Alexei Andreevich, Saratov State University
Abstract: 

The paper reproduces basic results concerning transition to chaos via destruction of quasiperiodic motion in one-dimensional circle map. For the golden mean rotation number we present the renormalization group (RG) analysis, consider structure of the critical attractor, give illustrations of scaling in the parameter space of the model map. 
We outline the fact that the two-parameter scaling can be observed only in a specially chosen local coordinates connected with the parameters of the original map via a nonlinear variable change; its form must account the concrete relation between two relevant eigenvalues of the linearized RG equation.

Key words: 
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Acknowledgments: 
The work was supported by the RFBR, grant № 00-02-17509 and Ministry of Education of the Russian Federation, grant № 97-0-8.3-88.
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Received: 
01.06.2000
Accepted: 
14.08.2000
Published: 
23.10.2000
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