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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Rational map has a Cantor Circle Julia set  and  a Sierpinski Carpet Julia set of degree m

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pp. 1483–1491Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1569XML
Published Online:
01 Nov 2023
Article type:
Research Article
Language:
EN
Article no.:
JIM-1569
Pages:
1483–1491

Abstract

This research aims to study complex dynamics, and one of the best examples of this concept is the Julia set, for this we will present new concepts specific to the Julia set of the rational map J(Gμ). We introduce the family of complex rational maps as:                Gμ(z) = 2μm+1 z–m + z2m – μ3m+1 / zm (z2m – μm–1) ,              with m ≥ 2 and  μ ϵ ℂ\{0}(ℂ complex numbers) such that μm+1 ≠ 1 and μ2m+2 ≠ 1. We prove  J(Gμ) is a degenerate Sierpinski carpet or a Sierpinski carpet or a Cantor circle by condition  one of the free critical points has an image for Gμ  is diverge on  ∞ or 0.

Keywords

Subject Classifications

Primary 37F50Secondary 37P40

References

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