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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