University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Alternating Period-Doubling Cascades

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

Text (licence)

Download (33kB)
Aston-text3a.pdf - ["content_typename_Accepted version (post-print)" not defined]
Available under License : See the attached licence file.

Download (366kB) | Preview


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 :
Aston, PJ
Bristow, N
Date : 6 August 2013
DOI : 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 : 31 Oct 2017 15:09

Actions (login required)

View Item View Item


Downloads per month over past year

Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800