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Alternating Period-Doubling Cascades

Aston, PJ and Bristow, N (2013) Alternating Period-Doubling Cascades Nonlinearity, 26 (9). pp. 2553-2576.

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We consider period-doubling cascades in two-dimensional iterated maps. We define forward and backward period-doubling bifurcations, and use these concepts to describe an alternating period-doubling cascade in which forward and backward period-doubling bifurcations alternate. By tracking the eigenvalues of a typical map throughout such cascades we show that two-dimensional maps may give rise to two qualitatively different alternating period-doubling cascades. We apply renormalisation theory to one class of alternating period-doubling cascades, and derive universal spatial scalings for such cascades from fixed points of the appropriate renormalisation operator. We also derive universal parameter scalings for these cascades from the eigenvalues of the linearisation of the renormalisation operator, and provide the corresponding eigenfunctions. The theory is illustrated by an example.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 6 August 2013
Identification Number : 10.1088/0951-7715/26/9/2553
Additional Information : Copyright 2013 Institute of Physics.
Depositing User : Symplectic Elements
Date Deposited : 02 Dec 2015 11:27
Last Modified : 02 Dec 2015 11:27

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