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 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
UTAS Author:	Delbourgo, R (Professor Robert Delbourgo)
UTAS 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
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