Abstract
For a certain class of piecewise monotonic transformations it is shown using a spectral decomposition of the Perron-Frobenius-operator ofT that invariant measures depend continuously on 3 types of perturbations: 1) deterministic perturbations, 2) stochastic perturbations, 3) randomly occuring deterministic perturbations. The topology on the space of perturbed transformations is derived from a metric on the space of Perron-Frobenius-operators.
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Keller, G. Stochastic stability in some chaotic dynamical systems. Monatshefte für Mathematik 94, 313–333 (1982). https://doi.org/10.1007/BF01667385
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DOI: https://doi.org/10.1007/BF01667385