{"paper":{"title":"Shadowing for nonautonomous dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Davor Dragicevic, Lucas Backes","submitted_at":"2018-03-16T21:15:43Z","abstract_excerpt":"We prove that whenever a sequence of invertible and bounded operators $(A_m)_{m\\in \\mathbb{Z}}$ acting on a Banach space $X$ admits an exponential dichotomy and a sequence of differentiable maps $f_m \\colon X\\to X$, $m\\in \\mathbb{Z}$, has bounded and H\\\"{o}lder derivatives, the nonautonomous dynamics given by $x_{m+1}=A_mx_m+f_m(x_m)$, $m\\in \\mathbb{Z}$ has various shadowing properties. Hence, we extend recent results of Bernardes Jr. et al. in several directions. As a nontrivial application of our results, we give a new proof of the nonautonomous Grobman-Hartman theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06402","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"}