On Transfer Operators and Maps with Random Holes
Dynamical Systems
2015-06-19 v2
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.
Cite
@article{arxiv.1405.0361,
title = {On Transfer Operators and Maps with Random Holes},
author = {Wael Bahsoun and Joerg Schmeling and Sandro Vaienti},
journal= {arXiv preprint arXiv:1405.0361},
year = {2015}
}