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

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....

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Bibliographic Details
Published in:arXiv.org 2019-01
Main Authors: Garibaldi, Eduardo, Inoquio-Renteria, Irene
Format: Article
Language:English
Subjects:
Optimization
Online Access:Get full text
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Summary: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.
ISSN:2331-8422