Thermodynamic formalism and $k$-bonacci substitutions

Jordan Emme (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 AMU - Aix Marseille Université

We study $k$-bonacci substitutions. For each 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.

Domaines: Systèmes dynamiques [math.DS]; Combinatoire [math.CO]

Jordan Emme. Thermodynamic formalism and $k$-bonacci substitutions. Discrete and Continuous Dynamical Systems - Series A, 2017, 37 (7), pp.3701 - 3719. ⟨10.3934/dcds.2017157⟩. ⟨hal-01278883v2⟩