We extend the Killeen-Taylor study [Nonlinearity 13 (2000)] by investigating in different Banach spaces (,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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-1-3,
author = {el Houcein el Abdalaoui and Ali Messaoudi},
title = {On the spectrum of stochastic perturbations of the shift and Julia sets},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {47-68},
zbl = {1269.47004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-1-3}
}
el Houcein el Abdalaoui; Ali Messaoudi. On the spectrum of stochastic perturbations of the shift and Julia sets. Fundamenta Mathematicae, Tome 219 (2012) pp. 47-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-1-3/