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

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

2011-09-30

arxiv.org/abs/1109.6899v1

Mathematics

Dynamical Systems

24 pages, 8 figures and 10 references

Scientific paper

We extend the Killeen-Taylor study in \cite{KT} by investigating in different Banach spaces ($\ell^\alpha(\N), c_0(\N),c_c(\N)$) 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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