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arXiv · 2308.14485

H\"older continuity of measures for heavy tail potentials

Godofredo Iommi·Dalia Terhesiu·Mike Todd
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Abstract

For a class of potentials $\psi$ satisfying a condition depending on the roof function of a suspension (semi)flow, we show an EKP inequality, which can be interpreted as a H\"older continuity property in the weak${^*}$ norm of measures, with respect to the pressure of those measures, where the H\"older exponent depends on the $L^q$-space that $\psi$ belongs to. This also captures a new type of phase transition for intermittent (semi)flows (and maps).

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Godofredo Iommi, Dalia Terhesiu, Mike Todd. 2023-08-28. H\"older continuity of measures for heavy tail potentials. https://doi.org/10.1017/etds.2024.139

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