Abstract
Let $A$ be a complex Banach algebra, $f:A\rightarrow A$ be a polynomial function with coefficients in $A$. We define the Julia set of f, denoted by J(f). We give conditions which often determine in which set, $J(f)$ or $A\setminus J(f)$, the periodic point lies. We show that the closure of repelling periodic points is not always equals the Julia set. However, we use the theorem of Gelfand-Mazur to characterize the algebras where it's true.
Citation
M. Aamri. A. Attioui. A. Azhari. "Itération des polynômes dans une algèbre de Banach." Bull. Belg. Math. Soc. Simon Stevin 10 (4) 551 - 559, December 2003. https://doi.org/10.36045/bbms/1070645801
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