Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle

We prove quantitative statistical stability results for a large class of small $C^{0}$ perturbations of circle diffeomorphisms with irrational rotation numbers. We show that if the rotation number is Diophantine the invariant measure varies in a Hölder way under perturbation of the map and the Hölder exponent depends on the Diophantine type of the rotation number. The set of admissable perturbations includes the ones coming from spatial discretization and hence numerical truncation. We also show...