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Islands of stability and complex universality relations


Delbourgo, R and Hughes, P and Kenny, BG, Islands of stability and complex universality relations, Journal of Mathematical Physics, 28, (1) pp. 60-63. ISSN 0022-2488 (1987) [Refereed Article]

DOI: doi:10.1063/1.527808


For complex mappings of the type z→λz(1−z), universality constants α and δ can be defined along islands of stability lying on filamentary sequences in the complex λ plane. As the end of the filament is approached, asymptotic values α N ∼λ N−1 ∞, δ N /α2 N ∼1 are attained, where μ∞=λ∞(λ∞−2)/4, is associated with the limiting form of the universal function for that sequence, g(z)=1−μ∞ z 2. These results are complex generalizations of the real mapping case (applying to tangent bifurcations and windows of stability) where μ∞=2 and δ/α2→ (2)/(3) correspond to the filament running along the real axis.

Item Details

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:90713
Year Published:1987
Web of Science® Times Cited:1
Deposited By:Mathematics and Physics
Deposited On:2014-04-16
Last Modified:2014-04-16

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