{"paper":{"title":"Almost sure convergence of maxima for chaotic dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. T\\\"or\\\"ok, M. Nicol, M.P. Holland","submitted_at":"2015-10-15T19:46:51Z","abstract_excerpt":"Suppose $(f,\\mathcal{X},\\nu)$ is a measure preserving dynamical system and $\\phi:\\mathcal{X}\\to\\mathbb{R}$ is an observable with some degree of regularity. We investigate the maximum process $M_n:=\\max\\{X_1,\\ldots,X_n\\}$, where $X_i=\\phi\\circ f^i$ is a time series of observations on the system. When $M_n\\to\\infty$ almost surely, we establish results on the almost sure growth rate, namely the existence (or otherwise) of a sequence $u_n\\to\\infty$ such that $M_n/u_n\\to 1$ almost surely. The observables we consider will be functions of the distance to a distinguished point $\\tilde{x}\\in \\mathcal{X"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04681","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":""},"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"}