Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior

In this paper, by applying Petković’s iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter <i<r</i< and research the stability of this method by using complex dynamics tools on the...
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Autor*in:	Xiaofeng Wang [verfasserIn] Wenshuo Li [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	nonlinear equations Julia and Fatou sets Mandelbrot set dynamics analysis parameter space dynamical plane

Übergeordnetes Werk:	In: Fractal and Fractional - MDPI AG, 2018, 6(2022), 12, p 749
Übergeordnetes Werk:	volume:6 ; year:2022 ; number:12, p 749

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DOI / URN:	10.3390/fractalfract6120749

Katalog-ID:	DOAJ083171207

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520			\|a In this paper, by applying Petković’s iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter <i<r</i< and research the stability of this method by using complex dynamics tools on the basis of fractal theory. Through analyzing the stability of the fixed point and drawing the parameter space related to the critical point, the parameter family which can make the behavior of the corresponding iterative method stable or unstable is obtained. Lastly, the consequence is verified by showing their corresponding dynamical planes.
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language	English
source	In Fractal and Fractional 6(2022), 12, p 749 volume:6 year:2022 number:12, p 749
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callnumber-first	Q - Science
author	Xiaofeng Wang
spellingShingle	Xiaofeng Wang misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc nonlinear equations misc Julia and Fatou sets misc Mandelbrot set misc dynamics analysis misc parameter space misc dynamical plane misc Thermodynamics misc Mathematics misc Analysis Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior
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topic_title	QC310.15-319 QA1-939 QA299.6-433 Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior nonlinear equations Julia and Fatou sets Mandelbrot set dynamics analysis parameter space dynamical plane
topic	misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc nonlinear equations misc Julia and Fatou sets misc Mandelbrot set misc dynamics analysis misc parameter space misc dynamical plane misc Thermodynamics misc Mathematics misc Analysis
topic_unstemmed	misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc nonlinear equations misc Julia and Fatou sets misc Mandelbrot set misc dynamics analysis misc parameter space misc dynamical plane misc Thermodynamics misc Mathematics misc Analysis
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title	Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior
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title_sort	choosing the best members of the optimal eighth-order petković’s family by its fractal behavior
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title_auth	Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior
abstract	In this paper, by applying Petković’s iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter <i<r</i< and research the stability of this method by using complex dynamics tools on the basis of fractal theory. Through analyzing the stability of the fixed point and drawing the parameter space related to the critical point, the parameter family which can make the behavior of the corresponding iterative method stable or unstable is obtained. Lastly, the consequence is verified by showing their corresponding dynamical planes.
abstractGer	In this paper, by applying Petković’s iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter <i<r</i< and research the stability of this method by using complex dynamics tools on the basis of fractal theory. Through analyzing the stability of the fixed point and drawing the parameter space related to the critical point, the parameter family which can make the behavior of the corresponding iterative method stable or unstable is obtained. Lastly, the consequence is verified by showing their corresponding dynamical planes.
abstract_unstemmed	In this paper, by applying Petković’s iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter <i<r</i< and research the stability of this method by using complex dynamics tools on the basis of fractal theory. Through analyzing the stability of the fixed point and drawing the parameter space related to the critical point, the parameter family which can make the behavior of the corresponding iterative method stable or unstable is obtained. Lastly, the consequence is verified by showing their corresponding dynamical planes.
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title_short	Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior
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