Different types of scaling in the dynamics of period–doubling maps under external periodic driving

N. Yu. Ivank’ov and S. P. Kuznetsov

Discrete Dynamics in Nature and Society, 2000, vol. 5, 1-10

Abstract:

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: F -scaling (Feigenbaum’s) for finite binary fractions, P - and Q -scaling (periodic and quasiperiodic) for periodic binary fractions, and S -scaling (statistical) for non-periodic binary fractions. All types of scaling are illustrated by parameter-plane diagrams for the rescaled Lyapunov exponent.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:781025

DOI: 10.1155/S1026022600000546

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