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Ratio ergodic theorems for mapswith indifferent fixed points

Published online by Cambridge University Press:  01 June 1997

TOMOKI INOUE
Affiliation:
Section of Applied Mathematics, Department of Computer Science, Faculty of Engineering, Ehime University, Matsuyama 790-77, Japan
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Abstract

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We study one-dimensional transformations $T$ with indifferent fixed points$p$ and $q$ ($p$ and $q$ are fixed points with $ T^{\prime}(p) =T^{\prime}(q) = 1 $). In the case when $T$ has a Lebesgue equivalent infiniteinvariant measure, we give the ratio ergodic theorems which describe thelimit value of the ratio of the sojourn time of the trajectory$\{T^k(x)\}_{k=0}^n$ in a small neighborhood of $p$ to that in a smallneighborhood of $q$.

Information

Type
Research Article
Copyright
1997 Cambridge University Press