Stefano Luzzatto: Statistical Properties of Doubly Intermittent Maps

Abstract: We introduce a class of full branch one-dimensional maps with two neutral fixed points as well as critical points and/or singularities, which significantly generalise the standard and well known intermittency maps. We extend many known results to these families but also show that a relatively large subclass of such maps have “historic” or “non-statistical” behaviour and thus in particular have no physical measure. This is joint work with Douglas Coates and Muhammad Mubarak.