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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.
keywords:
Thermodynamic formalism
,
word combinatorics
,
substitutions
,
pressure function
,
symbolic dynamics
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