Adam Chapman ; Solomon Vishkautsan
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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)
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https://doi.org/10.46298/cm.9042
Roots and Dynamics of Octonion PolynomialsArticle
Authors: Adam Chapman ; Solomon Vishkautsan
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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.