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

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el Abdalaoui e., Messaoudi A.

Fundamenta Mathematicae

2012

tom 218

nr 1

47-68

We extend the Killeen-Taylor study [Nonlinearity 13 (2000)] by investigating in different Banach spaces ($ℓ^{α}(ℕ)$,c₀(ℕ),c(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 ℂ².

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Messaoudi A.

1 el Abdalaoui e.

1 2012

Wyniki wyszukiwania

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