Expanding maps of an interval with holes

  title={Expanding maps of an interval with holes},
  author={Henry van den Bedem and N. Chernov},
We study a class of open chaotic dynamical systems. Consider an expanding map of an interval from which a few small open subintervals are removed (thus creating “holes”). Almost every point of the original interval then eventually escapes through the holes, so there can be no absolutely continuous invariant measures. We construct a so called conditionally invariant measure that is equivalent to the Lebesgue measure. Our measure is unique and naturally generates an invariant measure, which is… CONTINUE READING
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