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We consider iteration of arithmetic and power means and discuss methods for determining their limit. These means appear naturally in connection with some problems in homogenization theory.
Let be a disjoint iteration semigroup of diffeomorphisms mapping a real open interval onto . It is proved that if has a dense orbit possesing a subset of the second category with the Baire property, then for some diffeomorphism of onto the set of all reals . The paper generalizes some results of J.A.Baker and G.Blanton [3].
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