On the spectrum of stochastic perturbations of the shift and Julia sets

Volume 218 / 2012

el Houcein el Abdalaoui, Ali Messaoudi Fundamenta Mathematicae 218 (2012), 47-68 MSC: Primary 47A10, 47A35; Secondary 37F50, 37A30. DOI: 10.4064/fm218-1-3


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 $\mathbb C^2$.


  • el Houcein el AbdalaouiDepartment of Mathematics
    University of Rouen
    LMRS, UMR 60 85
    Avenue de l'Université, BP. 12
    76801 Saint Étienne du Rouvray, France
  • Ali MessaoudiDepartamento de Matemática
    Rua Cristovõ Colombo, 2265
    CEP 15054-0000
    São José de Rio Preto, SP, Brasil

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