Douglas Coates

Hausdorff dimension of sets of generic points for non-statistical interval maps

Consider an interval map that is expanding except at some finite number of neutral fixed points where the derivative is exactly 1. If such a map has several neutral fixed points which are "equally sticky" and "sufficiently sticky" then the map admits non-statistical behaviour. This means that the sequence of empirical measures does not converge for a typical initial condition. In particular there are no invariant measures whose basin of attraction has positive Lebesgue measure. In this talk we will examine sets of points for which the empirical measures do converge. We will show that there is a simplex of invariant measures where each measure has a basin of attraction of full Hausdorff dimension. This is joint work with Katrin Gelfert UFRJ.