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Quasi-invariant measures, escape rates and the effect of the hole

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  • Let $T$ be a piecewise expanding interval map and $T_H$ be an abstract perturbation of $T$ into an interval map with a hole. Given a number , 0 < < l, we compute an upper-bound on the size of a hole needed for the existence of an absolutely continuous conditionally invariant measure (accim) with escape rate not greater than -ln(1-). The two main ingredients of our approach are Ulam's method and an abstract perturbation result of Keller and Liverani.
    Mathematics Subject Classification: Primary 37A05, 37E05.


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