Hölder continuity of measures for heavy tail potentials

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 Hölder continuity property in the weak ${^*}$ norm of measures, with respect to the pressure of those measures, where the Hölder exponent depends on the $L^q$ -space to which $\psi $ belongs. This also captures a new type of phase transition for intermittent (semi)flows (and maps).

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Publication Details

Journal
Ergodic Theory and Dynamical Systems
Published
2025-01-22
DOI
https://doi.org/10.1017/etds.2024.139
Primary Topic
Quantum chaos and dynamical systems
Type
article
Field-Weighted Citation Impact
0.00

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article

Hölder continuity of measures for heavy tail potentials

Mike Todd, Dalia Terhesiu, Godofredo Iommi
Ergodic Theory and Dynamical Systems
Quantum chaos and dynamical systems
article

Hölder continuity of measures for heavy tail potentials

Mike Todd, Dalia Terhesiu, Godofredo Iommi
article en

Abstract

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 Hölder continuity property in the weak ${^*}$ norm of measures, with respect to the pressure of those measures, where the Hölder exponent depends on the $L^q$ -space to which $\psi $ belongs. This also captures a new type of phase transition for intermittent (semi)flows (and maps).

Ergodic Theory and Dynamical SystemsVol. 45(8)
Leiden University (NL), Pontificia Universidad Católica de Chile (CL), University of St Andrews (GB)
Erwin Schrödinger International Institute for Mathematics and Physics, Pontificia Universidad Católica de Chile, Fundação para a Ciência e a Tecnologia, Fondo Nacional de Desarrollo Científico y Tecnológico
Openalex Percentile: Top 99%
Quantum chaos and dynamical systems
DOIOpen Access PDFOpenAlex
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Hölder continuity of measures for heavy tail potentials — Mike Todd, Dalia Terhesiu, et al. · Ergodic Theory and Dynamical Systems (2025) | TGRS Research Map | TGRS