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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MDPI AG
2025-01-01
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| 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. |
| format | Article |
| id | doaj-art-e1b0989217fc4a43accc7ebf6024b5af |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| 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 |