Entropy of Hidden Markov Processes and Connections to Dynamical Systems: On the preservation of Gibbsianness under symbol amalgamation

@inproceedings{Chazottes2011EntropyOH,
  title={Entropy of Hidden Markov Processes and Connections to Dynamical Systems: On the preservation of Gibbsianness under symbol amalgamation},
  author={J. R. Chazottes and Edgardo Ugalde},
  year={2011}
}
Starting from the full-shift on a finite alphabet A, mingling some symbols of A, we obtain a new full shift on a smaller alphabet B. This amal- gamation defines a factor map from (A N ,TA) to (B N ,TB), where TA and TB are the respective shift maps. According to the thermodynamic formalism, to each regular function ('poten- tial') : A N ! R, we can associate a unique Gibbs measure µ . In this article, we prove that, for a large class of potentials, the pushforward measureµ � � 1 is still… CONTINUE READING

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