94-63 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) Mar 14, 94

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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.

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