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Invariant densities for random systems of the interval
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 42 / Issue 1 / January 2022
- Published online by Cambridge University Press:
- 29 December 2020, pp. 141-179
- Print publication:
- January 2022
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- Article
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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. If 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.
