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# Islands of stability and complex universality relations

journal contribution

posted on 2023-05-17, 23:52 authored by Robert DelbourgoRobert Delbourgo, Hughes, P, Kenny, BGFor complex mappings of the type z→λz(1−z), universality constants α and δ can be defined along islands of stability lying on filamentary sequences in the complex λ plane. As the end of the filament is approached, asymptotic values α N ∼λ N−1 ∞, δ N /α2 N ∼1 are attained, where μ∞=λ∞(λ∞−2)/4, is associated with the limiting form of the universal function for that sequence, g(z)=1−μ∞ z 2. These results are complex generalizations of the real mapping case (applying to tangent bifurcations and windows of stability) where μ∞=2 and δ/α2→ (2)/(3) correspond to the filament running along the real axis.

## History

## Publication title

Journal of Mathematical Physics## Volume

28## Pagination

60-63## ISSN

0022-2488## Department/School

School of Natural Sciences## Publisher

Amer Inst Physics## Place of publication

Circulation & Fulfillment Div, 2 Huntington Quadrangle, Ste 1 N O 1, Melville, USA, Ny, 11747-4501## Repository Status

- Restricted