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Induced maps, Markov extensions and invariant measures in one-dimensional dynamics. (English) Zbl 0827.58015
The paper deals with interval maps $$f : I \to I$$ that are piecewise continuous and piecewise monotone. The relation of induced maps $$F$$ to $$f$$ in the sense that $$F$$ coincides on certain subintervals with iterates of $$f$$ and the Markov extension of $$f$$ is discussed. For the case that $$f$$ is a non-flat $$S$$-unimodal map the author gives a simple inequality as a necessary condition for $$f$$ to have an absolutely continuous invariant probability measure.

##### MSC:
 3.7e+100 Low-dimensional dynamical systems
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##### References:
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