The pressure function for infinite equilibrium measures
MetadataShow full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
Assume 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.
Bruin , H , Terhesiu , D & Todd , M 2019 , ' The pressure function for infinite equilibrium measures ' , Israel Journal of Mathematics , vol. 232 , no. 2 , pp. 775-826 . https://doi.org/10.1007/s11856-019-1887-1
Israel Journal of Mathematics
© 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 https://doi.org/10.1007/s11856-019-1887-1
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.