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.

Publication Title

Communications in Mathematical Physics