Generating Special Curves for Cubic Polynomials

Khudoyor Mamayusupov, Figen Çilingir, Marks Ruziboev, Gafurjan Ibragimov and Bruno Antonio Pansera ()
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Khudoyor Mamayusupov: Department of Mathematics, New Uzbekistan University, Movarounnahr 1, Tashkent 100007, Uzbekistan
Figen Çilingir: Department of Mathematics, Faculty of Arts and Sciences, Iğdır University, Iğdır 76100, Turkey
Marks Ruziboev: School of Engineering, Central Asian University, 264, Milliy bog St, Tashkent 111221, Uzbekistan
Gafurjan Ibragimov: V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent 100174, Uzbekistan
Bruno Antonio Pansera: Department of Law, Economics and Human Sciences & Decisions_Lab, University Mediterranea of Reggio Calabria, I-89124 Reggio Calabria, Italy

Mathematics, 2025, vol. 13, issue 3, 1-17

Abstract: 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.

Keywords: critical orbit relations; resultant; recurrence relation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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