Projection of Markov measures may be Gibbsian

Details Projection of Markov measures may be Gibbsian Projection of Markov measures may be Gibbsian

2002-11-29

arxiv.org/abs/math/0211457v1

Mathematics

Dynamical Systems

4 latex figures

Scientific paper

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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