{"paper":{"title":"Invariant distributions of partially hyperbolic systems: fractal graphs, excessive regularity, and rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Disheng Xu, Jiesong Zhang","submitted_at":"2024-11-29T12:38:35Z","abstract_excerpt":"We introduce a novel approach linking fractal geometry to partially hyperbolic dynamics, revealing several new phenomena related to regularity jumps and rigidity. One key result demonstrates a sharp phase transition for partially hyperbolic diffeomorphisms $f \\in \\mathrm{Diff}^\\infty_{\\mathrm{vol}}(\\mathbb{T}^3)$ with a contracting center direction: $f$ is $C^\\infty$-rigid if and only if both $E^s$ and $E^c$ exhibit H\\\"older exponents exceeding the expected threshold. Specifically, we prove:\n  If the H\\\"older exponent of $E^s$ exceeds the expected value, then $E^s$ is $C^{1+}$ and $E^u \\oplus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19665","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.19665/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"}