Hermodynamic formalism and k-bonacci substitutions

Jordan Emme

doi:10.3934/dcds.2017157

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2017, Volume 37, Issue 7: 3701-3719. Doi: 10.3934/dcds.2017157

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Hermodynamic formalism and k-bonacci substitutions

Jordan Emme

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

Received: June 30, 2016

Revised: January 31, 2017

Published: August 2017

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Abstract

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.

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

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