{"paper":{"title":"Density of spectral gap property for positively expansive dynamics and smooth potentials, with applications to the phase transition problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Thiago Bomfim, Victor Carneiro","submitted_at":"2025-05-29T18:32:56Z","abstract_excerpt":"It is known that all uniformly expanding dynamics $f: M \\rightarrow M$ have no phase transition with respect to a H\\\"older continuous potential $\\phi : M \\rightarrow \\mathbb{R}$, in other words, the topological pressure function $\\mathbb{R} \\ni t \\mapsto P_{top}(f , t\\phi)$ is analytical. Moreover, the associated transfer operator $\\mathcal{L}_{f , t\\phi}$, acting on the space of H\\\"older continuous functions, has the spectral gap property for $t \\in \\mathbb{R}$. For dynamics that are topologically conjugate to an expanding map, a full understanding has yet to be achieved. On the one hand, by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23934","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.23934/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}