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Relations between universal scaling constants for the circle map near the golden mean

Citation

Delbourgo, R and Kenny, BG, Relations between universal scaling constants for the circle map near the golden mean, Journal of Mathematical Physics, 32, (4) pp. 1045-1051. ISSN 0022-2488 (1991) [Refereed Article]

DOI: doi:10.1063/1.529382

Abstract

The two‐frequency quasiperiodic route to chaos is believed to be modeled by the critical circle map and the universal behavior of the scaling constants α and δ is determined by the order z of the inflection point. We have numerically determined α(z) and δ(z) as a function of this order. Using the renormalization group equations, we have succeeded in obtaining approximate analytical relations for α and δ that agree quite well with the data. In the limit as z→∞, we argue that ‖δ‖→1/ρ3=4.236 and δ/α z →1, in good agreement with the numerical computations.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Atomic, Molecular, Nuclear, Particle and Plasma Physics
Research Field:Particle Physics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Physical Sciences
Author:Delbourgo, R (Professor Robert Delbourgo)
Author:Kenny, BG (Mr Brian Kenny)
ID Code:90698
Year Published:1991
Web of Science® Times Cited:5
Deposited By:Mathematics and Physics
Deposited On:2014-04-16
Last Modified:2014-04-16
Downloads:0

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