# Generic invariant measures for iterated systems of interval homeomorphisms

@article{Czernous2019GenericIM,
title={Generic invariant measures for iterated systems of interval homeomorphisms},
author={Wojciech Czernous and Tomasz Z. Szarek},
journal={Archiv der Mathematik},
year={2019},
volume={114},
pages={445-455}
}
• Published 31 May 2019
• Mathematics
• Archiv der Mathematik
It is well known that iterated function systems generated by orientation preserving homeomorphisms of the unit interval with positive Lyapunov exponents at its ends admit a unique invariant measure on (0, 1) provided their action is minimal. With the additional requirement of continuous differentiability of maps on a fixed neighbourhood of $$\{0,1\}$$ { 0 , 1 } , we present a metric in the space of such systems which renders it complete. Using then a classical argument (and an alternative…
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