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Typical points for one-parameter families of piecewise expanding maps of the interval

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  • For one-parameter families of piecewise expanding maps of the interval we establish sufficient conditions such that a given point in the interval is typical for the absolutely continuous invariant measure for a full Lebesgue measure set of parameters. In particular, we consider $C^{1,1}(L)$-versions of $\beta$-transformations, piecewise expanding unimodal maps, and Markov structure preserving one-parameter families. For families of piecewise expanding unimodal maps we show that the turning point is almost surely typical whenever the family is transversal.
    Mathematics Subject Classification: Primary: 37E05, 37A05; Secondary: 37D20.


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