A LARGE DEVIATION PRINCIPLE FOR THE EQUILIBRIUM STATES OF HÖLDER POTENTIALS: THE ZERO TEMPERATURE CASE

• DOI: 10.1142/s0219493706001657
• Publication Date: 2006-03-07T11:18:34Z
• Authors: ALEXANDRE BARAVIERA; ARTUR O. LOPES; PHILIPPE THIEULLEN
• Keywords: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]; 0101 mathematics; 01 natural sciences

Consider a α-Hölder function A : Σ → ℝ and assume that it admits a unique maximizing measure μmax. For each β, we denote μβ, the unique equilibrium measure associated to βA. We show that (μβ) satisfies a Large Deviation Principle, that is, for any cylinder C of Σ, [Formula: see text] where [Formula: see text] where V(x) is any strict subaction of A.