Publicação: On the spectrum of stochastic perturbations of the shift and Julia sets
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Polish Acad Sciences Inst Mathematics
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Resumo
We extend the Killeen-Taylor study [Nonlinearity 13 (2000)] by investigating in different Banach spaces (l(alpha)(N), c(0)(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 C-2.
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Markov operator, Markov process, Transition operator, stochastic perturbations of the shift, Stochastic adding machine, Julia set, residual spectrum, continuous spectrum
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Inglês
Como citar
Fundamenta Mathematicae. Warsaw 10: Polish Acad Sciences Inst Mathematics, v. 218, n. 1, p. 47-68, 2012.
