{"paper":{"title":"Extremal dichotomy for uniformly hyperbolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Maria Carvalho, Mark Holland, Matthew Nicol","submitted_at":"2015-01-20T23:51:02Z","abstract_excerpt":"We consider the extreme value theory of a hyperbolic toral automorphism $T: \\mathbb{T}^2 \\to \\mathbb{T}^2$ showing that if a H\\\"older observation $\\phi$ which is a function of a Euclidean-type distance to a non-periodic point $\\zeta$ is strictly maximized at $\\zeta$ then the corresponding time series $\\{\\phi\\circ T^i\\}$ exhibits extreme value statistics corresponding to an iid sequence of random variables with the same distribution function as $\\phi$ and with extremal index one. If however $\\phi$ is strictly maximized at a periodic point $q$ then the corresponding time-series exhibits extreme "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05023","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"}