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Generating Special Curves for Cubic Polynomials

Author

Listed:
  • Khudoyor Mamayusupov

    (Department of Mathematics, New Uzbekistan University, Movarounnahr 1, Tashkent 100007, Uzbekistan
    These authors contributed equally to this work.)

  • Figen Çilingir

    (Department of Mathematics, Faculty of Arts and Sciences, Iğdır University, Iğdır 76100, Turkey
    These authors contributed equally to this work.)

  • Marks Ruziboev

    (School of Engineering, Central Asian University, 264, Milliy bog St, Tashkent 111221, Uzbekistan
    These authors contributed equally to this work.)

  • Gafurjan Ibragimov

    (V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent 100174, Uzbekistan
    Department of Econometrics, Tashkent State University of Economics, Tashkent 100066, Uzbekistan
    Department of International Scientific Journals and Rankings, Alfraganus University, Yukori Karakamish Street 2a, Tashkent 100190, Uzbekistan
    These authors contributed equally to this work.)

  • Bruno Antonio Pansera

    (Department of Law, Economics and Human Sciences & Decisions_Lab, University Mediterranea of Reggio Calabria, I-89124 Reggio Calabria, Italy
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Khudoyor Mamayusupov & Figen Çilingir & Marks Ruziboev & Gafurjan Ibragimov & Bruno Antonio Pansera, 2025. "Generating Special Curves for Cubic Polynomials," Mathematics, MDPI, vol. 13(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:401-:d:1576996
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