By analyzing the functional equations governing N replication for real nonlinear maps on the (unit) interval (of order z), we have derived the asymptotic (N-->∞) behaviors of the scaling constants alpha and delta, alpha(z)~(2z)(N-1)/(z-1), delta/alphaz=(z-1)/(z-1/2). In addition, we have determined the limiting forms of the universal functions. The predictions are in excellent agreement with (separately compiled) numerical data over a wide range of z values and cycle structures.

Item Type:	Refereed Article
Research Division:	Physical Sciences
Research Group:	Particle and high energy physics
Research Field:	Particle physics
Objective Division:	Expanding Knowledge
Objective Group:	Expanding knowledge
Objective Field:	Expanding knowledge in the physical sciences
UTAS Author:	Delbourgo, R (Professor Robert Delbourgo)
UTAS Author:	Kenny, BG (Mr Brian Kenny)
ID Code:	90857
Year Published:	1986
Web of Science® Times Cited:	14
Deposited By:	Mathematics and Physics
Deposited On:	2014-04-29
Last Modified:	2014-04-29
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