Generic invariant measures for iterated systems of interval homeomorphisms

  title={Generic invariant measures for iterated systems of interval homeomorphisms},
  author={Wojciech Czernous and Tomasz Z. Szarek},
  journal={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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