Invariant densities for random systems of the interval

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 Lüroth maps with a hole.

References in corpus (1)

• Local dimensions for the random beta-transformation

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