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Hermodynamic formalism and k-bonacci substitutions

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  • We study k-bonacci substitutions through the point of view of thermodynamic formalism. For each substitution we define a renormalization operator associated to it and examine its iterates over potentials in a certain class. We also study the pressure function associated to potentials in this class and prove the existence of a freezing phase transition which is realized by the only ergodic measure on the subshift associated to the substitution.

    Mathematics Subject Classification: Primary: 37D35, 37B10; Secondary: 37C30.


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