Generating Special Curves for Cubic Polynomials

An algorithmic method is proposed to generate all cubic polynomials with a critical orbit relation. We generate curves (polynomials of parameters) that correspond to those functions with critical orbit relations. The irreducibility of the polynomials obtained is left as an open problem. Our approach...

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Main Authors: Khudoyor Mamayusupov, Figen Çilingir, Marks Ruziboev, Gafurjan Ibragimov, Bruno Antonio Pansera
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/3/401
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author Khudoyor Mamayusupov
Figen Çilingir
Marks Ruziboev
Gafurjan Ibragimov
Bruno Antonio Pansera
author_facet Khudoyor Mamayusupov
Figen Çilingir
Marks Ruziboev
Gafurjan Ibragimov
Bruno Antonio Pansera
author_sort Khudoyor Mamayusupov
collection DOAJ
description An algorithmic method is proposed to generate all cubic polynomials with a critical orbit relation. We generate curves (polynomials of parameters) that correspond to those functions with critical orbit relations. The irreducibility of the polynomials obtained is left as an open problem. Our approach also works to generate critical orbit relations in all families of rational functions with active critical points.
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institution DOAJ
issn 2227-7390
language English
publishDate 2025-01-01
publisher MDPI AG
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spelling doaj-art-e1b0989217fc4a43accc7ebf6024b5af2025-08-20T02:48:02ZengMDPI AGMathematics2227-73902025-01-0113340110.3390/math13030401Generating Special Curves for Cubic PolynomialsKhudoyor Mamayusupov0Figen Çilingir1Marks Ruziboev2Gafurjan Ibragimov3Bruno Antonio Pansera4Department of Mathematics, New Uzbekistan University, Movarounnahr 1, Tashkent 100007, UzbekistanDepartment of Mathematics, Faculty of Arts and Sciences, Iğdır University, Iğdır 76100, TurkeySchool of Engineering, Central Asian University, 264, Milliy bog St, Tashkent 111221, UzbekistanV.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent 100174, UzbekistanDepartment of Law, Economics and Human Sciences & Decisions_Lab, University Mediterranea of Reggio Calabria, I-89124 Reggio Calabria, ItalyAn algorithmic method is proposed to generate all cubic polynomials with a critical orbit relation. We generate curves (polynomials of parameters) that correspond to those functions with critical orbit relations. The irreducibility of the polynomials obtained is left as an open problem. Our approach also works to generate critical orbit relations in all families of rational functions with active critical points.https://www.mdpi.com/2227-7390/13/3/401critical orbit relationsresultantrecurrence relation
spellingShingle Khudoyor Mamayusupov
Figen Çilingir
Marks Ruziboev
Gafurjan Ibragimov
Bruno Antonio Pansera
Generating Special Curves for Cubic Polynomials
Mathematics
critical orbit relations
resultant
recurrence relation
title Generating Special Curves for Cubic Polynomials
title_full Generating Special Curves for Cubic Polynomials
title_fullStr Generating Special Curves for Cubic Polynomials
title_full_unstemmed Generating Special Curves for Cubic Polynomials
title_short Generating Special Curves for Cubic Polynomials
title_sort generating special curves for cubic polynomials
topic critical orbit relations
resultant
recurrence relation
url https://www.mdpi.com/2227-7390/13/3/401
work_keys_str_mv AT khudoyormamayusupov generatingspecialcurvesforcubicpolynomials
AT figencilingir generatingspecialcurvesforcubicpolynomials
AT marksruziboev generatingspecialcurvesforcubicpolynomials
AT gafurjanibragimov generatingspecialcurvesforcubicpolynomials
AT brunoantoniopansera generatingspecialcurvesforcubicpolynomials