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Stability of the distribution function for piecewise monotonic maps on the interval

The research was partially supported by the projects 42p11 and 38p10 of AKTION Česká republika – Österreich, and by RVO funding for IČ47813059.

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  • For piecewise monotonic maps the notion of approximating distribution function is introduced. It is shown that for a mixing basic set it coincides with the usual distribution function. Moreover, it is proved that the approximating distribution function is upper semi-continuous under small perturbations of the map.

    Mathematics Subject Classification: 37E05, 37D45, 37C75.


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