{"paper":{"title":"Shy shadows of infinite-dimensional partially hyperbolic invariant sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.FA"],"primary_cat":"math.DS","authors_text":"Daniel Smania","submitted_at":"2015-08-29T02:50:31Z","abstract_excerpt":"Let $\\mathcal{R}$ be a strongly compact $C^2$ map defined in an open subset of an infinite-dimensional Banach space such that the image of its derivative $D_F \\mathcal{R}$ is dense for every $F$. Let $\\Omega$ be a compact, forward invariant and partially hyperbolic set of $\\mathcal{R}$ such that $\\mathcal{R}\\colon \\Omega\\rightarrow \\Omega$ is onto. The $\\delta$-shadow $W^s_\\delta(\\Omega)$ of $\\Omega$ is the union of the sets $$W^s_\\delta(G)= \\{F\\colon dist(\\mathcal{R}^iF, \\mathcal{R}^iG) \\leq \\delta, \\ for \\ every \\ i\\geq 0 \\},$$ where $G \\in \\Omega$. Suppose that $W^s_\\delta(\\Omega)$ has tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07388","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"}