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

  title={Dynamical obstruction to the existence of continuous sub-actions for interval maps with regularly varying property},
  author={Eduardo Garibaldi and Irene Inoquio-Renteria},
  journal={Discrete \& Continuous Dynamical Systems - A},
In ergodic optimization theory, the existence of sub-actions is an important tool in the study of the so-called optimizing measures. For transformations with regularly varying property, we highlight a class of moduli of continuity which is not compatible with the existence of continuous sub-actions. Our result relies fundamentally on the local behavior of the dynamics near a fixed point and applies to interval maps that are expanding outside an indifferent fixed point, including Manneville… 
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