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

2011/09/30 by El Houcein El Abdalaoui, E. H. El Abdalaoui, Abdalaoui, E. H. El +3
Mathematics · #37A30 #37F50 #47A10 #47A35 #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Spectral Theory in Mathematical Physics #math.DS #msc:37A30 #msc:37F50 #msc:47A10 #msc:47A35

paper · pdf · doi:10.48550/arxiv.1109.6899

24 pages, 8 figures and 10 references

arxiv created 2011/09/30 · openalex publication_date 2011/09/30 · arxiv updated 2011/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the Killeen-Taylor study in \citeKT by investigating in different Banach spaces (ℓ^α(\N), c₀(\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 \C².

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