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arXiv · 1109.6899

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

E. H. El Abdalaoui·A. Messaoudi
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Abstract

We extend the Killeen-Taylor study in \cite{KT} by investigating in different Banach spaces ($\ell^α(\N), c_0(\N),c_c(\N)$) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the stochastic adding machine in base 2 and in Fibonacci base. For the base 2, the spectra are connected to the Julia set of a quadratic map. In the Fibonacci case, the spectra involve the Julia set of an endomorphism of $\C^2$.

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E. H. El Abdalaoui, A. Messaoudi. 2011-09-30. On the spectrum of stochastic perturbations of the shift and Julia sets. https://arxiv.org/abs/1109.6899

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