Projection of Markov measures may be Gibbsian

2002/11/29 by J. -R. Chazottes, Chazottes, J. -R., E. Ugalde +1 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.math/0211457

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arxiv created 2002/11/29 · arxiv updated 2009/11/30

Abstract

We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs measure (in the sense of Bowen) when the factor system is again a topological Markov chain. This amounts to constructing, when it does exist, the induced potential and proving its Holder continuity. This is achieved through a matrix method. We provide examples and counterexamples to illustrate our results.

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