On Transfer Operators and Maps with Random Holes
arXiv:1405.0361 · doi:10.1088/0951-7715/28/3/713
Abstract
We study Markov interval maps with random holes. The holes are not necessarily elements of the Markov partition. Under a suitable, and physically relevant, assumption on the noise, we show that the transfer operator associated with the random open system can be reduced to a transfer operator associated with the closed deterministic system. Exploiting this fact, we show that the random open system admits a unique (meaningful) absolutely continuous conditionally stationary measure. Moreover, we prove the existence of a unique probability equilibrium measure supported on the survival set, and we study its Hausdorff dimension.
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