Ergodic type solutions of differential equations with piecewise constant arguments.
Absolutely continuous dynamics and real coboundary cocycles in -spaces, 0 < p < ∞
Conditions for the existence of measurable and integrable solutions of the cohomology equation on a measure space are deduced. They follow from the study of the ergodic structure corresponding to some families of bidimensional linear difference equations. Results valid for the non-measure-preserving case are also obtained
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