Ergodic properties of infinite measure-preserving interval maps with indifferent fixed points

We consider piecewise twice differentiable maps T on [0, 1] with indifferen t fixed points giving rise to infinite invariant measures, and we study the ir behaviour on ergodic components. As we do not assume the existence of a Markov partition but only require the first image of the fundamental partit ion to be finite, we use canonical Markov extensions to first prove pointwi se dual-ergodicity, which, together with an identification of wandering rat es, leads to distributional limit theorems. We show that T satisfies Rohlin 's formula and prove a variant of the Shannon-McMillan-Breiman theorem. Mor eover, we give a stronger limit theorem for the transfer operator providing us with a large collection of uniform and Darling-Kac sets. This enables u s to apply recent results from fluctuation theory.