Hölder continuity of measures for heavy tail potentials

Godofredo Iommi; Dalia Terhesiu; Mike Todd

doi:10.1017/etds.2024.139

Hölder continuity of measures for heavy tail potentials

Godofredo Iommi
, Dalia Terhesiu
, Mike Todd^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

For a class of potentials ψ 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 ψ belongs. This also captures a new type of phase transition for intermittent (semi)flows (and maps).

Original language	English
Number of pages	38
Journal	Ergodic Theory and Dynamical Systems
Volume	First View
Early online date	22 Jan 2025
DOIs	https://doi.org/10.1017/etds.2024.139
Publication status	E-pub ahead of print - 22 Jan 2025

Keywords

EKP-inequality
Gibbs-Markov maps
Suspension flows

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10.1017/etds.2024.139Licence: CC BY

Iommi_2025_ETaDS_Holder-continuity-heavy-tail-potentials_CC
© The Author(s), 2025. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Final published version, 474 KBLicence: CC BY

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title = "H{\"o}lder continuity of measures for heavy tail potentials",

abstract = "For a class of potentials ψ 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{\"o}lder continuity property in the weak∗ norm of measures, with respect to the pressure of those measures, where the H{\"o}lder exponent depends on the Lq-space to which ψ belongs. This also captures a new type of phase transition for intermittent (semi)flows (and maps).",

keywords = "EKP-inequality, Gibbs-Markov maps, Suspension flows",

author = "Godofredo Iommi and Dalia Terhesiu and Mike Todd",

note = "Funding: GI was partially supported by Proyecto Fondecyt 1230100. DT would like to thank Henk Bruin for discussions on related topics during the Research-in-Teams project 0223 {\textquotedblleft}Limit Theorems for Parabolic Dynamical Systems{\textquotedblright} at the Erwin Schr{\"o}dinger Institute, Vienna. MT would like to thank Pontificia Universidad Cat{\'o}lica de Chile where part of this research was done, supported by Proyecto Fondecyt 1230100, and thanks the University of Leiden for hosting a visit where part of this research was done. He is also partially supported by the FCT (Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia) project 2022.07167.PTDC.",

year = "2025",

month = jan,

day = "22",

doi = "10.1017/etds.2024.139",

language = "English",

volume = "First View",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

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TY - JOUR

T1 - Hölder continuity of measures for heavy tail potentials

AU - Iommi, Godofredo

AU - Terhesiu, Dalia

AU - Todd, Mike

N1 - Funding: GI was partially supported by Proyecto Fondecyt 1230100. DT would like to thank Henk Bruin for discussions on related topics during the Research-in-Teams project 0223 “Limit Theorems for Parabolic Dynamical Systems” at the Erwin Schrödinger Institute, Vienna. MT would like to thank Pontificia Universidad Católica de Chile where part of this research was done, supported by Proyecto Fondecyt 1230100, and thanks the University of Leiden for hosting a visit where part of this research was done. He is also partially supported by the FCT (Fundação para a Ciência e a Tecnologia) project 2022.07167.PTDC.

PY - 2025/1/22

Y1 - 2025/1/22

N2 - For a class of potentials ψ 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 Lq-space to which ψ belongs. This also captures a new type of phase transition for intermittent (semi)flows (and maps).

AB - For a class of potentials ψ 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 Lq-space to which ψ belongs. This also captures a new type of phase transition for intermittent (semi)flows (and maps).

KW - EKP-inequality

KW - Gibbs-Markov maps

KW - Suspension flows

U2 - 10.1017/etds.2024.139

DO - 10.1017/etds.2024.139

M3 - Article

SN - 0143-3857

VL - First View

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

ER -

Hölder continuity of measures for heavy tail potentials

Abstract

Keywords

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