A generic C1 expanding map has a singular S-R-B measure
We show that for a generic C1 expanding map T of the unit circle, there is a unique equilibrium state for - log T′ that is an S-R-B measure for T, and whose statistical basin of attraction has Lebesgue measure 1. We also present some results related to the question of whether a generic C1 expanding map preserves a σ-finite measure, absolutely continuous with respect to Lebesgue measure.
Communications in Mathematical Physics
Campbell, J., & Quas, A. (2001). A generic C1 expanding map has a singular S-R-B measure. Communications in Mathematical Physics, 221 (2), 335-349. https://doi.org/10.1007/s002200100491