Pre-threshold fractional susceptibility functions at Misiurewicz parameters

Abstract

We show that the response, frozen and semifreddo fractional susceptibility functions of certain real-analytic unimodal families, at Misiurewicz parameters and for fractional differentiation index 0 ≤ η < 1 2 , are holomorphic on a disk of radius greater than one. This is a step towards solving Conjecture A[i] in [5], in the case of the aforementioned susceptibility functions.