Pre-threshold fractional susceptibility functions at Misiurewicz parameters

Abstract

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 a conjecture of Baladi and Smania, in the case of the aforementioned susceptibility functions.