具有正则变化性质的区间映射存在连续子作用的动力学障碍
Dynamical obstruction to the existence of continuous sub-actions for interval maps with regularly varying property
摘要：
在遍历优化理论中，子作用的存在性是研究所谓优化措施的一个重要工具。对于具有规则变化性质的变换，我们强调一类与连续子动作的存在不兼容的连续模。我们的结果从根本上依赖于局部行为的动力学附近的一个不动点，并适用于区间地图，扩大以外的一个冷漠的不动点，包括Manneville-Pomeau和Farey地图。
英文摘要：
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.
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