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SPECTRUM OF STOCHASTIC ADDING MACHINES AND FIBERED JULIA SETS

Abstract : Consider the basic algorithm to perform the transformation n--> n + 1 changing digits of the d-adic expansion of n one by one. We obtain a family of Markov chains on the non-negative integers through successive and independent applications of the algorithm modified by a parametrized stochastic rule that randomly prevents one of the steps in the algorithm to finish. The objects of study in this paper are the spectra of the transition operators of these Markov chains. The spectra of these Markov chains turn out to be fibered Julia sets of fibered polynomials. This enables us to analyze their topological and analytical properties with respect to the underlying parameters of the Markov chains.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00795677
Contributor : Olivier Sester <>
Submitted on : Thursday, February 28, 2013 - 4:43:16 PM
Last modification on : Monday, October 19, 2020 - 2:34:03 PM

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Ali Messaoudi, Olivier Sester, Glauco Valle. SPECTRUM OF STOCHASTIC ADDING MACHINES AND FIBERED JULIA SETS. Stochastics and Dynamics, World Scientific Publishing, 2012, 13 (3), 1250021 (26 p.). ⟨10.1142/S0219493712500219⟩. ⟨hal-00795677⟩

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