# American Institute of Mathematical Sciences

May  2018, 38(5): 2527-2539. doi: 10.3934/dcds.2018105

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

 1 Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava, Czech Republic 2 Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

Received  August 2017 Revised  November 2017 Published  March 2018

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

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.

Citation: Michal Málek, Peter Raith. Stability of the distribution function for piecewise monotonic maps on the interval. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2527-2539. doi: 10.3934/dcds.2018105
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