A Ruelle–Perron–Frobenius theorem for expanding circle maps with an indifferent fixed point

We establish an original result for the thermodynamic formalism in context of expanding circle transformations with indifferent fixed point. For observable whose modulus continuity is linked to dynamics near such a point, by identifying appropriate linear space evaluate action transfer operator, we show that there strictly positive eigenfunction associated maximal eigenvalue given as exponential topological pressure. Taking into account also corresponding eigenmeasure, invariant probability thus obtained proved be unique Gibbs-equilibrium state system.