THE POTENTIAL POINT OF VIEW FOR RENORMALIZATION
Résumé
For the shift σ in Σ = {0, 1} ℕ , we define the renormalization for potentials by [Formula: see text] We show that for a good H, there is a unique fixed point for [Formula: see text]. It is the Hofbauer potential V*. We show that the stable set of the Hofbauer potential, i. e. the set of potentials V such that [Formula: see text] converges to V* is characterized by the germ of these potentials close to 0 ∞ = 000…. Then, we make connections with the Manneville–Pomeau map f : [0, 1]↺. In particular we show that the lift in Σ of log f′ is in the stable set of V*. In the second part, we characterize "good" H, such that σ 2 ◦ H = H ◦ σ. In the last part, we study the thermodynamic formalism for some special potentials in the stable set of V*. They are called virtual Manneville–Pomeau maps.