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Journal of Interdisciplinary Mathematics

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502
CiteScore 2025: 1.9 (Q2)

CiteScore 2025: 1.9 (Q2)

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Journal of Interdisciplinary Mathematics
Open Access Research Article

Julia sets are quasicircles for rational maps of degree N

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pp. 1421–1429Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1560XML
Published Online:
28 Oct 2023
Article type:
Research Article
Language:
EN
Article no.:
JIM-1560
Pages:
1421–1429

Abstract

This research aims to study complex dynamics, where the complex dynamic is considered a branch of dynamical systems, which takes maps from the Riemann sphere to the Riemann sphere. The Julia sets are also examples of fractals and the most important of them, thus being a fractal set. This work aims to study the Julia sets of a family of rational maps are quasicircles and offer the boundaries of the immediate basin of attraction of zero and the infinity are quasi-circles. Now, we introduce the family of  maps are defined as: Gb (z) = 2bn+1 z–n + z2n – b3n+1/zn (z2n – bn–1), (1) where  n ≥ 2  and  b ϵ ℂ\{0} also bn+1 ≠ 1 and b2n+2 ≠ 1.

Keywords

Julia setsFatou setFatou componentsQuasicirclesPerturbed

Subject Classifications

08C1520E10

References

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