{"paper":{"title":"Ergodic Transport Theory and Piecewise Analytic Subactions for Analytic Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OC"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Daniel Smania, Elismar R. Oliveira","submitted_at":"2012-05-25T17:23:07Z","abstract_excerpt":"We consider a piecewise analytic real expanding map $f: [0,1]\\to [0,1]$ of degree $d$ which preserves orientation, and a real analytic positive potential $g: [0,1] \\to \\mathbb{R}$. We assume the map and the potential have a complex analytic extension to a neighborhood of the interval in the complex plane. We also assume $\\log g$ is well defined for this extension.\n  It is known in Complex Dynamics that under the above hypothesis, for the given potential $\\beta \\,\\log g$, where $\\beta$ is a real constant, there exists a real analytic eigenfunction $\\phi_\\beta$ defined on $[0,1]$ (with a complex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5758","kind":"arxiv","version":1},"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"}