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Stochastic adding machines based on Bratteli diagrams. (Odomètres stochastiques associées aux diagrammes de Bratteli.) (English. French summary) Zbl 1469.37003

Summary: In this paper, we define some Markov chains associated with Vershik maps on Bratteli diagrams. We study probabilistic and spectral properties of their transition operators and we prove that the spectra of these operators are connected to Julia sets in higher dimensions. We also study topological properties of these spectra.

MSC:

37A30 Ergodic theorems, spectral theory, Markov operators
37B10 Symbolic dynamics
37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
37F80 Higher-dimensional holomorphic and meromorphic dynamics
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
47A10 Spectrum, resolvent
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