Itération des polynômes dans une algèbre de Banach
Attioui, A. ; Azhari, A. ; Aamri, M.
Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 551-559 / Harvested from Project Euclid
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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.
Publié le : 2003-09-14
Classification:  Itération,  polynôme,  point périodique,  théorie spectrale,  46J99,  30D05 
@article{1070645801,
     author = {Attioui, A. and Azhari, A. and Aamri, M.},
     title = {It\'eration des polyn\^omes dans une alg\`ebre de Banach},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {10},
     number = {1},
     year = {2003},
     pages = { 551-559},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/1070645801}
}

Attioui, A.; Azhari, A.; Aamri, M. Itération des polynômes dans une algèbre de Banach. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp.  551-559. http://gdmltest.u-ga.fr/item/1070645801/