| Abstract: |
| We consider a family of transformations and study a random dynamical system such that
one transformation is randomly selected from the family and then applied on each iteration.
For this kind of random dynamical systems, we study the first return random map
and make clear the relation between an invariant measure of the first return random map and
it of the original random map.
We apply our result to the random iterations of
one-dimensional maps with indifferent fixed points and study invariant measures for these random maps.
In this talk,
we give a result on the existence of absolutely continuous sigma-finite invariant measures.
After that, we give a condition such that the sigma-finite invariant measure of a random map is a finite measure. We also give a condition such that the sigma-finite invariant measure of it is an infinite measure. |
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