From infinite ergodic theory to number theory (and possibly back)

Some basic facts of infinite ergodic theory are reviewed in a form suitable to be applied to interval maps with number theoretic significance such as the Farey map. This is an enlarged version of the lecture notes accompanying a short course on Infinite Ergodic Theory at the First meeting of the (mostly) young italian hyperbolicians (Corinaldo, Italy, June 8–12, 2009).

► Systems preserving an infinite measure need new indicators such as the wandering rate.
► Coping wild behaviour of the ergodic sums with very good sets and universal sequences.
► Applications to Farey map and slow convergents in continued fractions theory.