Article contents
Ratio ergodic theorems for mapswith indifferent fixed points
Published online by Cambridge University Press: 01 June 1997
Abstract
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 infinite invariant measure, we give the ratio ergodic theorems which describe the limit 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 small neighborhood of $q$.
- Type
- Research Article
- Information
- Copyright
- 1997 Cambridge University Press
- 6
- Cited by