N. Yu. Ivank’ov, S. P. Kuznetsov, "Different types of scaling in the dynamics of period–doubling maps under external periodic driving", Discrete Dynamics in Nature and Society, vol. 5, Article ID 781025, 10 pages, 2000. https://doi.org/10.1155/S1026022600000546
Different types of scaling in the dynamics of period–doubling maps under external periodic driving
Based on the renormalization group approach developed by Kuznetsov and Pikovsky (Phys. Lett., A140, 1989, 166) several types of scaling are discussed, which can be observed in a neighborhood of Feigenbaum’s critical point at small amplitudes of the driving. The type of scaling behavior depends on a structure of binary representation of the frequency parameter: -scaling (Feigenbaum’s) for finite binary fractions, - and -scaling (periodic and quasiperiodic) for periodic binary fractions, and -scaling (statistical) for non-periodic binary fractions. All types of scaling are illustrated by parameter-plane diagrams for the rescaled Lyapunov exponent.
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