{"paper":{"title":"Thermodynamic formalism and Substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nicolas Bedaride, Pascal Hubert, Renaud Leplaideur","submitted_at":"2015-11-10T22:39:16Z","abstract_excerpt":"This paper studies properties of a Renormalization Operator for potentials in symbolic dynamics. These operators first appeared in \\cite{BLL} and the link with substitutions was done in \\cite{BL1}. Their fixed points are natural candidates to have pathologic behavior such as phase transitions. If $R$ is such an operator, we study the convergence of $R^{n}(\\varphi)$ to the non-nul fixed point.\n  We define the family of marked substitutions, which contains the Thue-Morse substitution, and show that the associated renormalization operators on potentials admits a unique non-nul continuous fixed po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03322","kind":"arxiv","version":2},"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"}