Statistical properties of one-dimensional expanding maps with singularities of low regularity (Q2000193)

This paper studies the statistical properties of a class of piecewise expanding interval maps where the inverse Jacobian possibly has low regularity close to singularities. The authors prove that a map \(F\) in the class preserves a unique SRB measure \(\mu\) which is absolutely continuous with respect to Lebesgue measure and its corresponding density function is positive and continuous except on a countable set. They obtain certain statistical properties for maps \(F\) in the class of piecewise Hölder functions with the unique SRB measure \(\mu\) from above. Their approach uses the functional analytic method of \textit{M. F. Demers} and \textit{H.-K. Zhang} [J. Mod. Dyn. 5, No. 4, 665--709 (2011; Zbl 1321.37034)].