Substitution shifts and renormalization for potentials

 Motivated by Bowen's theory of thermodynamic formalism of
subshifts of finite type, Hofbauer started to create symbolic models with
non-Hoelder potentials as simple examples exhibiting phase transitions.
Hofbauer's examples relate directly to the Pomeau-Manneville map, which
Baraviera-Leplaideur-Lopes related again to a particular
substitution-based renormalization operator. In this talk, I want to
report on joint work with Leplaideur how this scheme extends to
non-trivial substitutions (Thue-Morse and Fibonacci), and discuss the
importance and properties of the fixed points of the renormalization
operator, their stable leaves, and connections to renormalization theory
in one-dimensional dynamics.