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.
Infinite invariant measures for non uniformly expanding transformations of [0,1]: weak law of large numbers with anomalous scaling
ISOLA, Stefano
1996-01-01
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.File in questo prodotto:
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