For citation:
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
Scaling at the transition to chaos via destruction of quasiperiodic motion at the golden mean frequency ratio
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.
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