Abstract

In this note, we establish an original result for the thermodynamicformalism in the context of expanding circle transformations with an indifferent fixedpoint. For an observable whose continuity modulus is linked to the dynamics near sucha fixed point, by identifying an appropriate linear space to evaluate the action of thetransfer operator, we show that there is a strictly positive eigenfunction associatedwith the maximal eigenvalue given as the exponential of the topological pressure.Taking into account also the corresponding eigenmeasure, the invariant probabilitythus obtained is proved to be the unique Gibbs-equilibrium state of the system.