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arXiv · 2112.14984

Quenched linear response for smooth expanding on average cocycles

Davor Dragičević·Paolo Giulietti·Julien Sedro
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Abstract

We establish an abstract quenched linear response result for random dynamical systems, which we then apply to the case of smooth expanding on average cocycles on the unit circle. In sharp contrast to the existing results in the literature, we deal with the class of random dynamics that does not necessarily exhibit uniform decay of correlations. Our techniques rely on the infinite-dimensional ergodic theory and in particular, on the study of the top Oseledets space of a parametrized transfer operator cocycle.

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Davor Dragičević, Paolo Giulietti, Julien Sedro. 2022-10-29. Quenched linear response for smooth expanding on average cocycles. https://doi.org/10.1007/s00220-022-04560-1

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