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Relations between universal scaling constants for the circle map near the golden mean
journal contribution
posted on 2023-05-17, 23:51 authored by Robert DelbourgoRobert Delbourgo, Kenny, BGThe 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.
History
Publication title
Journal of Mathematical PhysicsVolume
32Issue
4Pagination
1045-1051ISSN
0022-2488Department/School
School of Natural SciencesPublisher
American Institute of PhysicsPlace of publication
Melville, USARepository Status
- Restricted