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arXiv · 2503.16088

General real measurable Liv\v{s}ic regularity via transfer operators

Ian D. Morris
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Abstract

We prove a general measurable Liv\v{s}ic regularity theorem for real-valued cocycles over non-invertible dynamical systems using only abstract hypotheses on an associated transfer operator. As illustrative applications we derive measurable Liv\v{s}ic regularity results in the analytic regularity class for cocycles over real-analytic expanding maps, in the bounded-variation regularity class for $\beta$-transformations, and in $C^\alpha$ regularity over the class of virtually expanding maps recently introduced by M. Tsujii.

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Ian D. Morris. 2025-03-20. General real measurable Liv\v{s}ic regularity via transfer operators. https://arxiv.org/abs/2503.16088

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