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On the number of all absolutely continuous, ergodic measures of Markov type transformations defined on an interval. (English) Zbl 0622.28014

Let \(\phi\) be a Markov, piecewise monotonic transformation from an interval (bounded or unbounded) into itself. In this paper, the author considers the problem of determining the number of absolutely continuous ergodic measures of \(\phi\). The results improve the results of Kowalski, Li and Yorke, and Pianigiani.
Reviewer: A.Boyarsky

MSC:

28D10 One-parameter continuous families of measure-preserving transformations
37A99 Ergodic theory
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References:

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