Campanino M., Isola S.
Infinite invariant measures for non-uniformly expanding transformations of $[0,1]$:
weak law of large numbers with anomalous scaling.
(38K, TeX)
ABSTRACT. We consider a class of maps of $[0,1]$ with an indifferent fixed point at $0$
and expanding everywhere else.
Using the invariant ergodic probability measure
of a suitable, everywhere expanding, induced transformation
we are able to study the infinite invariant measure
of the original map in some detail.
Given a continuous function with compact support in $]0,1]$,
we prove that its time averages satisfy a `weak law of large numbers'
with anomalous scaling $n/\log n$ and give an upper bound for the decay of
correlations.