Dynamical obstruction to the existence of continuous sub-actions for interval maps with regularly varying property
Dynamical Systems
2019-01-23 v2
Abstract
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-Pomeau and Farey maps.
Cite
@article{arxiv.1809.00441,
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= {arXiv preprint arXiv:1809.00441},
year = {2019}
}