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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, BG
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.

History

Publication title

Journal of Mathematical Physics

Volume

32

Issue

4

Pagination

1045-1051

ISSN

0022-2488

Department/School

School of Natural Sciences

Publisher

American Institute of Physics

Place of publication

Melville, USA

Repository Status

  • Restricted

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