Geodesic
On the spectrum of stochastic perturbations of the shift and Julia sets
el Houcein el Abdalaoui 1   ; Ali Messaoudi 2
1 Department of Mathematics University of Rouen LMRS, UMR 60 85 Avenue de l'Université, BP. 12 76801 Saint Étienne du Rouvray, France
2 Departamento de Matemática IBILCE-UNESP Rua Cristovõ Colombo, 2265 CEP 15054-0000 São José de Rio Preto, SP, Brasil
Fundamenta Mathematicae, Tome 218 (2012) no. 1, pp. 47-68 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We extend the Killeen–Taylor study [Nonlinearity 13 (2000)] by investigating in different Banach spaces ($\ell^\alpha(\mathbb N), c_0(\mathbb N),c(\mathbb N)$) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the stochastic adding machine in base $2$ and in the Fibonacci base. For the base $2$, the spectra are connected to the Julia set of a quadratic map. In the Fibonacci case, the spectrum is related to the Julia set of an endomorphism of $\mathbb C^2$.
DOI : 10.4064/fm218-1-3
Keywords: extend killeen taylor study nonlinearity investigating different banach spaces ell alpha mathbb mathbb mathbb point continuous residual spectra stochastic perturbations shift operator associated stochastic adding machine base fibonacci base base spectra connected julia set quadratic map fibonacci spectrum related julia set endomorphism nbsp mathbb

el Houcein el Abdalaoui  1   ; Ali Messaoudi  2

1 Department of Mathematics University of Rouen LMRS, UMR 60 85 Avenue de l'Université, BP. 12 76801 Saint Étienne du Rouvray, France
2 Departamento de Matemática IBILCE-UNESP Rua Cristovõ Colombo, 2265 CEP 15054-0000 São José de Rio Preto, SP, Brasil 
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el Houcein el Abdalaoui; Ali Messaoudi. On the spectrum of stochastic perturbations of the shift and Julia sets. Fundamenta Mathematicae, Tome 218 (2012) no. 1, pp. 47-68. doi: 10.4064/fm218-1-3

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