RENORMALIZATION AND THERMODYNAMIC FORMALISM IN SUBSHIFTS.
Résumé
We examen thermodynamic formalism for a class renormalizable dynamical systems which in the symbolic space is generated by the Thue-Morse substitution, and in complex dynamics by the Feigenbaum map. The basic question answered is whether fixed points $V$ of a renormalization operator $\CR$ acting on the space of potentials are such that $\gamma \mapsto \CP(-\gamma V)$ exhibits phase transition. This extends the work by Baraviera, Leplaideur and Lopes on the Manneville-Pomeau map, where such phase transitions were indeed detected. In this paper, however, the attractor of renormalization is a Cantor set (rather than a single fixed point), which admits various classes of fixed points for $\CR$, some of which do and some of which do not exhibit phase transitions.
Origine : Fichiers produits par l'(les) auteur(s)