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

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.

keywords: Thermodynamic formalism word combinatorics substitutions pressure function symbolic dynamics

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