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In ergodic optimization theory, the existence of sub-actions is an importanttool in the study of the so-called optimizing measures. For transformationswith regularly varying property, we highlight a class of moduli of continuitywhich is not compatible with the existence of continuous sub-actions. Ourresult relies fundamentally on the local behavior of the dynamics near a fixedpoint and applies to interval maps that are expanding outside an indifferentfixed point, including Manneville-Pomeau and Farey maps.

Dynamical obstruction to the existence of continuous sub-actions for interval maps with regularly varying property