{"paper":{"title":"The pressure function for infinite equilibrium measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dalia Terhesiu, Henk Bruin, Mike Todd","submitted_at":"2017-11-14T12:02:25Z","abstract_excerpt":"Assume that $(X,f)$ is a dynamical system and $\\phi:X \\to [-\\infty, \\infty)$ is a potential such that the $f$-invariant measure $\\mu_\\phi$ equivalent to $\\phi$-conformal measure is infinite, but that there is an inducing scheme $F = f^\\tau$ with a finite measure $\\mu_{\\bar\\phi}$ and polynomial tails $\\mu_{\\bar\\phi}(\\tau \\geq n) = O(n^{-\\beta})$, $\\beta \\in (0,1)$. We give conditions under which the pressure of $f$ for a perturbed potential $\\phi+s\\psi$ relates to the pressure of the induced system as $P(\\phi+s\\psi) = (C P(\\overline{\\phi+s\\psi}))^{1/\\beta} (1+o(1))$, together with estimates for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05069","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}