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

• Autorzy: el Houcein el Abdalaoui , Ali Messaoudi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets
• 37A30: Ergodic theorems, spectral theory, Markov operators
• 47A35: Ergodic theory
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 218
• Numer: 1
• Strony: 47-68

Daty

wydano

2012

Twórcy

autor

el Houcein el Abdalaoui

• Department of Mathematics, University of Rouen, LMRS, UMR 60 85, Avenue de l'Université, BP. 12, 76801 Saint Étienne du Rouvray, France

autor

Ali Messaoudi

• Departamento de Matemática, IBILCE-UNESP, Rua Cristovõ Colombo, 2265, CEP 15054-0000, São José de Rio Preto, SP, Brasil

Identyfikatory

DOI

10.4064/fm218-1-3