Abstract

In the context of expanding maps of the circle with an indifferent fixed point, understanding the joint behavior of dynamics and pairs of moduli of continuity ( ω , Ω ) may be a useful element for the development of equilibrium theory. Here we identify a particular feature of modulus Ω (precisely lim x → 0 + sup d Ω ( d x ) / Ω ( d ) = 0 ) as a sufficient condition for the system to exhibit exponential decay of correlations with respect to the unique equilibrium state associated with a potential having ω as modulus of continuity. This result is derived from obtaining the spectral gap property for the transfer operator acting on the space of observables with Ω as modulus of continuity, a property that, as is well known, also ensures the Central Limit Theorem. Examples of application of our results include the Manneville-Pomeau family.