arXiv:1511.03322 Abstract | arXiv Analytics

arXiv:1511.03322 [math.DS]Abstract References Reviews Resources

Thermodynamic formalism and Substitutions

Nicolas Bedaride, Pascal Hubert, Renaud Leplaideur

Published 2015-11-10Version 1

We consider the class of marked substitutions. For a substitution in this class we examine the renormalization operator determined by it. Then we study the thermodynamic formalism for potentials in some class, and prove they have a freezing phase transition, with ground state supported on the attracting quasi-crystal associated to the substitution.

Comments: 43 pages, 6 figures

Categories: math.DS

Keywords: thermodynamic formalism, renormalization operator, freezing phase transition, ground state, marked substitutions

Related articles: Most relevant | Search more

arXiv:1309.7934 [math.DS] (Published 2013-09-30)

Renormalization, Freezing Phase Transitions and Fibonacci Quasicrystals

Henk Bruin, Renaud Leplaideur

arXiv:2505.04780 [math.DS] (Published 2025-05-07)

Thermodynamic Formalism Out of Equilibrium, and Gibbs Processes

Snir Ben Ovadia, Federico Rodriguez-Hertz

arXiv:2311.09397 [math.DS] (Published 2023-11-15)

Thermodynamic formalism for correspondences