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July  2017, 37(7): 3701-3719. doi: 10.3934/dcds.2017157

## Hermodynamic formalism and k-bonacci substitutions

 Aix-Marseille University, I2M, UMR 7373, 13 453 Marseille, France

Received  July 2016 Revised  February 2017 Published  April 2017

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.

Citation: Jordan Emme. Hermodynamic formalism and k-bonacci substitutions. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3701-3719. doi: 10.3934/dcds.2017157
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