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

Author(s)

el Abdalaoui, el Houcein ^[1] ; Messaoudi, Ali ^[2]

Affiliation

^[1] Univ Rouen, LMRS, UMR 60 85, Dept Math, F-76801 St Etienne - France

^[2] IBILCE UNESP, Dept Matemat, BR-15054000 Sao Jose De Rio Preto, SP - Brazil

• Document type: Journal article
• Source: FUNDAMENTA MATHEMATICAE; v. 218, n. 1, p. 47-68, 2012.
• Web of Science Citations: 6

Abstract

We extend the Killeen-Taylor study {[}Nonlinearity 13 (2000)] by investigating in different Banach spaces (l(alpha)(N), c(0)(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 C-2. (AU)

• FAPESP's process: 11/23199-1 - Dynamics of endomofisms of C2 and Julia sets
• Grantee: André Salles de Carvalho
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil