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

Michal Málek; Peter Raith

doi:10.3934/dcds.2018105

Article Contents

2018, Volume 38, Issue 5: 2527-2539. Doi: 10.3934/dcds.2018105

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

Michal Málek^1, and
Peter Raith^2,

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: July 31, 2017

Revised: October 31, 2017

Published: June 2018

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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Abstract

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.

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

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References

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