The recurrence time for ergodic systems with infinite invariant measures

We investigate quantitative recurrence in systems having an infinite invariant measure. We extend the Ornstein–Weiss theorem for a general class of infinite systems estimating return time in decreasing sequences of cylinders. Then we restrict to a class of one-dimensional maps with indifferent fixed points and calculate quantitative recurrence in sequences of balls, obtaining that this is related to the behaviour of the map near the fixed points