@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 -
