Orestis Georgiou, Carl P. Dettmann, Eduardo G. Altmann
We investigate the dependence of the escape rate on the position of a hole placed in uniformly hyperbolic systems admitting a finite Markov partition. We derive an exact periodic orbit formula which differs from other periodic expansions in the literature and can account for additional distortion to maps with a constant expansion rate. We apply this formula to show that for systems conjugate to the binary shift, the average escape rate is always larger than the expectation based on the hole size. Moreover, we show that the difference between the two decays like a known constant times the square of the hole size. Finally, we relate this problem to the random choice of holes and we discuss possible extensions of our results to non-Markov holes as well as applications to leaky dynamical networks.
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http://arxiv.org/abs/1207.7000
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