We consider random open dynamical systems. We obtain a first-order
perturbation formula in this setting, which allows us to treat various quantities like the escape rate, equilibrium states , limit theorems. Our new machinery is then deployed to create a spectral approach for a quenched extreme value theory that considers random dynamics with general ergodic invertible driving, and random observations. In collaboration with J. Atnip, G/ Froyland and C. Gonzalez-Tokman.
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