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arXiv · 1805.11430

Invariant densities for random systems of the interval

Charlene Kalle·Marta Maggioni
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Abstract

For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our procedure produces all invariant densities of the system. Examples include random tent maps, random W-shaped maps, random $\beta$-transformations and random L\"uroth maps with a hole.

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Charlene Kalle, Marta Maggioni. 2018-05-29. Invariant densities for random systems of the interval. https://doi.org/10.1017/etds.2020.127

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