Article

Generating Special Curves for Cubic Polynomials

Khudoyor MamayusupovDepartment of Mathematics, New Uzbekistan University, Movarounnahr 1, Tashkent 100007, UzbekistanFi̇gen Çi̇li̇ngi̇rDepartment of Mathematics, Faculty of Arts and Sciences, Iğdır University, Iğdır 76100, TurkeyMarks RuziboevGafurjan IbragimovDepartment of Econometrics, Tashkent State University of Economics, Tashkent 100066, UzbekistanBruno Antonio PanseraDepartment of Law, Economics and Human Sciences & Decisions_Lab, University Mediterranea of Reggio Calabria, I-89124 Reggio Calabria, Italy

Mathematicsjournal2025en

ABI

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.

Topics

Algebraic Geometry and Number Theory Polynomial and algebraic computation Meromorphic and Entire Functions

Identifiers

DOI: 10.3390/math13030401

Citations and references

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