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

el Houcein el Abdalaoui, and Ali Messaoudi. "On the spectrum of stochastic perturbations of the shift and Julia sets." Fundamenta Mathematicae 218.1 (2012): 47-68. <http://eudml.org/doc/286665>.

@article{elHouceinelAbdalaoui2012,
abstract = {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.},
author = {el Houcein el Abdalaoui, Ali Messaoudi},
journal = {Fundamenta Mathematicae},
keywords = {Markov operator; Markov process; stochastic adding machine; Julia sets; residual spectrum; continuous spectrum},
language = {eng},
number = {1},
pages = {47-68},
title = {On the spectrum of stochastic perturbations of the shift and Julia sets},
url = {http://eudml.org/doc/286665},
volume = {218},
year = {2012},
}

TY - JOUR
AU - el Houcein el Abdalaoui
AU - Ali Messaoudi
TI - On the spectrum of stochastic perturbations of the shift and Julia sets
JO - Fundamenta Mathematicae
PY - 2012
VL - 218
IS - 1
SP - 47
EP - 68
AB - 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.
LA - eng
KW - Markov operator; Markov process; stochastic adding machine; Julia sets; residual spectrum; continuous spectrum
UR - http://eudml.org/doc/286665
ER -