“Persistent” non-statistical behaviour for interval maps with neutral fixed points

Douglas Coates (Exeter)

I will present recent work joint with Stefano Luzzatto in which we study a class F of full branched maps admitting
two indifferent fixed points as well as critical points and/or unbounded derivative. We introduce a natural topology
on the class F and show that there is a dense subset G of maps which are non-statistical (and in particular which have
no physical measure). Moreover, we show that the non-statistical behaviour of the maps in G is "persistent"under
a particular class of perturbations.