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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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