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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:
37E99 Low-dimensional dynamical systems
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