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dc.contributor.authorBruin, Henk
dc.contributor.authorTerhesiu, Dalia
dc.contributor.authorTodd, Mike
dc.identifier.citationBruin , H , Terhesiu , D & Todd , M 2019 , ' The pressure function for infinite equilibrium measures ' , Israel Journal of Mathematics , vol. 232 , no. 2 , pp. 775-826 .
dc.identifier.otherPURE: 251533149
dc.identifier.otherPURE UUID: ca3e96d4-540f-45e3-949f-3d27d1785ba2
dc.identifier.otherORCID: /0000-0002-0042-0713/work/58755479
dc.identifier.otherScopus: 85070408851
dc.identifier.otherWOS: 000480562000009
dc.description.abstractAssume that (X,f) is a dynamical system and ϕ:X→[−∞,∞) is a potential such that the f-invariant measure μϕ equivalent to ϕ-conformal measure is infinite, but that there is an inducing scheme F=fτ with a finite measure μϕ¯ and polynomial tails μϕ¯(τ≥n) = O(n−β), β∈(0,1). We give conditions under which the pressure of f for a perturbed potential ϕ+sψ relates to the pressure of the induced system as P(ϕ+sψ) = (CP(ϕ+sψ))1/β(1+o(1)), together with estimates for the o(1)-error term. This extends results from Sarig to the setting of infinite equilibrium states. We give several examples of such systems, thus improving on the results of Lopes for the Pomeau-Manneville map with potential ϕt=−tlogf′, as well as on the results by Bruin & Todd on countably piecewise linear unimodal Fibonacci maps. In addition, limit properties of the family of measures μϕ+sψ as s→0 are studied and statistical properties (correlation coefficients and arcsine laws) under the limit measure are derived.
dc.relation.ispartofIsrael Journal of Mathematicsen
dc.rights© 2019, The Hebrew University of Jerusalem. This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at
dc.subjectQA Mathematicsen
dc.titleThe pressure function for infinite equilibrium measuresen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.description.statusPeer revieweden

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