poster: Thermodynamic Formalism and k-bonacci substitution
speaker: Jordan Emme (Institut de Mathématique d'Orsay)abstract: Given a dynamical system \((X,T)\) and a potential, this provides the pressure function. If we consider the full shift \((\Sigma,\sigma)\) on a finite alphabet and a substitution on this alphabet, we can define the Ruelle renormalization operator on continuous functions from \(\Sigma\) to \(\mathbb{R}\) (the potential is defined in terms of the distance to the subshift of the substitution). Bruin and Leplaideur have studied this renormalization on a certain family of potentials for the Thue-Morse and Fibonacci substitutions. They have also shown in this case the existence of non analytic points of the pressure function (called freezing phase transition points). These results have been extended by Bédaride, Hubert and Leplaideur to all marked substitutions with word combinatorics techniques. We generalize this to the family of \(k\)-bonacci substitutions.
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