On the fractional susceptibility function of piecewise expanding maps
We associate to a perturbation (ft) of a (stably mixing) piecewise expanding unimodal map f0 a two-variable fractional susceptibility function Ψφ(η, z), depending also on a bounded observable φ. For fixed η ∈ (0, 1), we show that the function Ψφ(η, z) is holomorphic in a disc Dη ⊂ C centered at zero of radius > 1, and that Ψφ(η, 1) is the Marchaud fractional derivative of order η of the function t
