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Morphology of the period-doubling universal function
journal contribution
posted on 2023-05-17, 23:51 authored by Roland WarnerRoland Warner, Robert DelbourgoRobert DelbourgoResults are presented concerning the structure on the real line of the "universal function" which is the fixed point solution of the Feigenbaum-Cvitanovic renormalization group equation associated with period-doubling chaos in quadratic maps. It is shown that the values which the function takes at its turning points can be algebraically characterized by relation to the infinite cycle associated with the original turning point of the map on the interval. These extreme become increasingly numerous as the argument increases, and their locations can be found progressively using knowledge of the previously determined extrema. As well as providing a simple understanding of the structure of the universal function these simple observations may be of assistance in investigating the convergence or asymptotic behavior of approximations to the universal function, and perhaps in providing a "corrector" step to some of these schemes.
History
Publication title
Journal of Mathematical PhysicsVolume
33Pagination
758-770ISSN
0022-2488Department/School
Institute for Marine and Antarctic StudiesPublisher
American Institute of PhysicsPlace of publication
Melville, USARepository Status
- Restricted