Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points

We consider piecewise twice differentiable maps T on [0,1] with indifferent fixed points giving rise to infinite invariant measures. Without assuming the existence of a Markov partition and only requiring that the first image of the fundamental partition is finite, we prove that the interval decomposes into a finite number of ergodic cycles with exact powers plus a dissipative part. T is shown to be exact on components containing indifferent fixed points. We also determine the order of the singularities of the invariant densities.