29 research outputs found
On the spectrum of stochastic perturbations of the shift and Julia sets
We extend the Killeen-Taylor study in \cite{KT} by investigating in different
Banach spaces () 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.Comment: 24 pages, 8 figures and 10 reference
Approximately transitive dynamical systems and simple spectrum
For some countable discrete torsion Abelian groups we give examples of their
finite measure-preserving actions which have simple spectrum and no approximate
transitivity property.Comment: 9 pages, Key words and phrases: ergodic theory, dynamical system, AT
property, funny rank one, Haar spectru