{"paper":{"title":"Uniform quasi-multiplicativity of locally constant cocycles and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Kiho Park, Reza Mohammadpour","submitted_at":"2022-09-19T13:25:34Z","abstract_excerpt":"In this paper, we show that a locally constant cocycle $\\mathcal{A}$ is $k$-quasi multiplicative under the irreducibility assumption. More precisely, we show that if $\\mathcal{A}^t$ and $\\mathcal{A}^{\\wedge m}$ are irreducible for every $t \\mid d$ and $1\\leq m \\leq d-1$, then $\\mathcal{A}$ is $k$-uniformly spannable for some $k\\in \\mathbb{N}$, which implies that $\\mathcal{A}$ is $k$-quasi multiplicative. We apply our results to show that the unique subadditive equilibrium Gibbs state is $\\psi$-mixing and calculate the Hausdorff dimension of cylindrical shrinking target and recurrence sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08999","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.08999/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"}