Abstract:For certain smooth unimodal families with negative Schwarzian derivative, we construct a set of Collet-Eckmann and subexponentially recurrent parameters Ω, whose complement set has sufficiently fast decaying density, on which exponential mixing with uniform rates occurs. We use this construction to establish holomorphy of the 'true' fractional susceptibility function of the logistic family, in a disk of radius larger than one, for differentiation index 0 ≤ η < 1/2, as recently conjectured by Baladi and Smania.… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.