{"paper":{"title":"Generalized hyperbolicity for diffeomorphisms of Banach spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Sergey Tikhomirov","submitted_at":"2025-10-07T01:35:51Z","abstract_excerpt":"We introduce generalized hyperbolicity for nonlinear dynamics in Banach spaces. The definition allows the stable/unstable splitting to be discontinuous and requires only inclusions, rather than equalities, in the invariance conditions for both subspaces. On smooth compact manifolds, generalized hyperbolicity is equivalent to Axiom~A and the strong transversality condition, providing a finite-dimensional calibration of the proposed Banach-space theory. For $C^1$-diffeomorphisms of the whole Banach space such that $Df$ and $D(f^{-1})$ are globally bounded and $Df$ is uniformly continuous, we est"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.05499","kind":"arxiv","version":3},"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/2510.05499/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"}