Adam Chapman ; Solomon Vishkautsan - Roots and Dynamics of Octonion Polynomials

cm:9042 - Communications in Mathematics, October 26, 2022, Volume 30 (2022), Issue 2 (Special Issue: CIMPA School "Nonassociative Algebras and Its Applications", Madagascar 2021) - https://doi.org/10.46298/cm.9042
Roots and Dynamics of Octonion Polynomials

Authors: Adam Chapman ; Solomon Vishkautsan

    This paper is devoted to several new results concerning (standard) octonion polynomials. The first is the determination of the roots of all right scalar multiples of octonion polynomials. The roots of left multiples are also discussed, especially over fields of characteristic not 2. We then turn to study the dynamics of monic quadratic real octonion polynomials, classifying the fixed points into attracting, repelling and ambivalent, and concluding with a discussion on the behavior of pseudo-periodic points.


    Volume: Volume 30 (2022), Issue 2 (Special Issue: CIMPA School "Nonassociative Algebras and Its Applications", Madagascar 2021)
    Published on: October 26, 2022
    Accepted on: February 3, 2022
    Submitted on: February 3, 2022
    Keywords: Mathematics - Rings and Algebras,Mathematics - Dynamical Systems,16S36, 16K20, 37P35, 37C25, 37F10

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